5. Arithmetic Progressions-Introduction of Arithmetic Progression Mathematics Class 10 In English-CBSE Notes
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5. Arithmetic Progressions-Introduction of Arithmetic Progression Mathematics Class 10 In English-CBSE Notes
5. Arithmetic Progressions
Introduction of Arithmetic Progression
Introduction of Arithmetic Progression
Arithmetic Progression: An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
Examples:
(a) 1, 2, 3, 4, 5 ......................................
(b) 2, 5, 8, 11, 14 ..................................
(c) 50, 45, 40, 35 .....................................
(d) -10, -4, 2, 8 .........................................
In above examples, each of the numbers in the list is called a term. Each term is obtained by adding a fixed number except the first term. And we can write other next term by adding same fixed number. This fixed number is called the common difference of the AP.
In other words, A list of numbers which has same common difference will be said Arithmetic progression.
- Each number of an arithmetic progression is called term.
- The first number of A.P is called first term.
- The last term of A.P is called final term.
- Difference between two consicutive terms of an A.P is known as common difference.
an = a + (n - 1)d पर आधारित प्रश्न :
Q1. Find the 21st term of A.P 9, 11, 13, 15, .........................
समांतर श्रेढ़ी 9, 11, 13, 15, ......................... का 21 वाँ पद ज्ञात कीजिए |
उत्तर : 49
Q2. Which term is 78 of A.P 3, 8, 13, 18, ..........................
A.P 3, 8, 13, 18, .......................... का कौन सा पद 78 है |
उत्तर : 16 वाँ पद
Q3. if 12, x and 22 are in A.P then find the value of x.
12, x, 22 A.P में है तो x का मान होगा ?
उत्तर : 17
Q4. Find the 12th term of A.P 3, 9, 15 ..................
A.P 3, 9, 15 .................. का 12 वाँ पद ज्ञात कीजिए |
उत्तर : 69
Q5. Find the expression for nth term of A.P: - 5, -2, 1, ..........................
समांतर श्रेढ़ी - 5, -2, 1, .......................... के n वाँ पद के लिए व्यंजक ज्ञात कीजिए |
उत्तर : 3n - 8
Q6. if three numbers 5, 2k - 3 and 9 are in A.P then find the value of x.
यदि तीन संख्याएँ 5, 2k - 3, 9 A.P में हैं तो k का मान ज्ञात कीजिए |
उत्तर : 5
Q7. Find the 9th term from last of the A. P: 7, 11, 15, .................... 147
स. श्रे. 7, 11, 15, .................... 147 का अंत से 9 वाँ पद ज्ञात कीजिए |
उत्तर : 115
Q8. Which term of A.P: 41, 38, 35, ...................... is the first negative?
स. श्रे. 41, 38, 35, ...................... का कौन सा पद ऋणात्मक है ?
उत्तर : 15 वाँ
Q9. Find first negative term of A.P: 41, 38, 35, ......................
स. श्रे. 41, 38, 35, ...................... का प्रथम ऋणात्मक पद ज्ञात कीजिए |
उत्तर : -1
Q10. Find common difference and 8th term of A.P: √2, √8, √18, √32, .............
A. P. √2, √8, √18, √32, -------------- का 8 वाँ पद एवं सार्व अंतर ज्ञात कीजिए |
उत्तर : √128, √2
Q11. The third and 9th term of an A.P are 4 and -8 respectively. Then find which term is zero?
यदि किसी A. P का तीसरा और नौवां पद 4 और - 8 है, तो इसका कौन सा पद शून्य है ?
उत्तर : 5 वाँ पद
Q12. Find the 31st term of an A.P whose 11th term is 38 and 16th term is 73.
उस A.P का 31 वाँ पद ज्ञात कीजिए जिसका 11 वाँ पद 38 है और 16 वाँ पद 73 है |
उत्तर :
Q13. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
किसी A.P का 17 वाँ पद उसके 10 वें पद से 7 अधिक है | तो इसका सार्व अंतर ज्ञात कीजिए |
उत्तर : 1
Q14. (i) For what value of n, are the nth terms of two APs: 63, 65, 67, . . .
and 3, 10, 17, . . . equal?
दो समांतर श्रेढियों 63, 65, 67, ..................... और 3, 10, 17, .................. के
n वाँ पद बराबर है तो n वाँ पद ज्ञात कीजिए |
उत्तर :
(ii) For what value of ‘n’, are the nth terms of two A.P.s 2, 10, 18, ......
and 68, 70, 72 ....... equal ? Also find the term.
n के किस मान के लिए दो समांतर श्रेढियों A.P.s 2, 10, 18, ...... तथा
68, 70, 72 ....... का nवाँ पद बराबर होगा ? पद भी ज्ञात कीजिए |
उत्तर :
Q15. How many three-digit numbers are divisible by 7?
तीन अंको वाली कितनी संख्याएँ 7 से विभाज्य हैं ?
उत्तर :
Q16. How many multiples of 5 are between 1 to 102?
1 से 102 के बीच 5 के गुनाजों की संख्या कितनी हैं ?
उत्तर :
Q17. How many multiples of 4 are between 10 to 250?
10 और 250 के बीच में 4 के गुणजों की संख्या कितनी हैं ?
उत्तर :
Q18. Find the A.P whose third term is -13 and sixth term is 2.
एक स. श्रे. ज्ञात कीजिए, जिसका तीसरा पद -13 और छठा पद 2 है |
उत्तर : –23, –18, –13, .......
Q19. How many three-digit numbers are divisible by 6?
तीन अंकों की कितनी संख्याएँ 6 से विभाज्य हैं ?
उत्तर :
Q20. How many three-digit numbers are divisible by 3?
तीन अंकों की कितनी संख्यायें 3 से विभाज्य हैं ?
उत्तर :
Q21. How many two-digit numbers are divisible by 7?
दो अंकों वाली कितनी संख्याएँ 6 से विभाज्य हैं ?
उत्तर : 15
Q22. if nth term of an A.P 4, 7, 10, ..................... is 82. Then find the value of n.
यदि एक A.P 4, 7, 10, ..................... का n वाँ पद 82 है, तो n का मान ज्ञात
कीजिए |
उत्तर : 27
Q23. if nth term of an A.P is 2n + 7, then find the 7th term of A.P.
यदि एक A.P का n वाँ पद 2n + 7 है, तो A.P का 7 वाँ पद ज्ञात कीजिए |
उत्तर : 21
Q24. if nth term of an A.P is 2n - 8, what term is zero of the A.P?
यदि एक A.P का n वाँ पद 2n - 8 है, तो A.P का कौन-सा पद शून्य है ?
उत्तर : 4
Q25. Find 25th term of an A.P if an = 3n - 2.
एक A.P का 25 वाँ पद ज्ञात कीजिए यदि an = 3n - 2 है |
उत्तर : 73
Q26. The final term of an A.P: 9, 17, 25, ................... is 601, find 35th term from final term.
A. P 9, 17, 25, ................... का अंतिम पद 601 है तो अंतिम पद से 35 वाँ पद
ज्ञात कीजिए |
उत्तर : 329
Q27. Which term will be zero of A.P: 105, 98, 91, ........................
A. P: 105, 98, 91, ........................ का कौन सा पद शून्य होगा |
उत्तर : 14
Q28. Find 41st term of an A.P if an = 3 - 4n.
एक A.P का 41 वाँ पद ज्ञात कीजिए यदि an = 3 - 4n है |
उत्तर : -161
Q29. FInd the numbers of all multiples of 4 between 19 to 101.
19 से 101 के बीच में आने वाले 4 के सभी गुणजों की संख्या ज्ञात कीजिए |
उत्तर : 21
Q30. if nth term of an A.P is 9 - 5n, then find the 21st term.
यदि एक A.P का n वाँ पद 9 - 5n है, तो A.P का 21 वाँ पद ज्ञात कीजिए |
उत्तर : - 96
Q31. If tn = 2n+1 then find the series (A.P).
यदि tn = 2n+1 है तो A.P ज्ञात कीजिए |
उत्तर :3, 5, 7, ....... 2n+1
Q32. Which term of the sequence 114, 109, 104…………is the first negative term?
समांतर श्रेढ़ी 114, 109, 104………… का कौन-सा पद पहला ऋणात्मक होगा ?
Q33. How many terms of A.P 18, 16, 14...Should be taken so that their sum is zero?
A.P 18, 16, 14............. के कितने पद लिए जाएँ ताकि उनका योग शून्य हो |
Q34. Which term of the A.P 21, 10, -1, - 12 ………. Will be 231 more than its 31st term?
A.P 21, 10, -1, - 12 ………. का कौन-सा पद इसके 31 वाँ पद से 231 अधिक होगा ?
Q35. Determine the AP whose 3rd term is 5 and the 7th term is 9.
समांतर श्रेढ़ी ज्ञात कीजिए जिसका तीसरा पद 5 तथा 7 वाँ पद 9 है |
Q36. How many two-digit numbers are divisible by 3?
दो अंकों की कितनी संख्या 3 से विभाज्य है ?
Q37. Find the 11th term from the last term (towards the first term) of the
AP : 10, 7, 4, . . ., – 62.
Q38. AP : 10, 7, 4, . . ., – 62 के अंतिम पद से (प्रथम पद की ओर) 11 वाँ पद ज्ञात कीजिए |
Q39. In a flower bed, there are 23 rose plants in the first row, 21 in the
second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
फूलों की एक क्यारी की पहली पंक्ति में 23 गुलाब के पौधे हैं, दूसरी पंक्ति में 21 गुलाब के पौधे हैं, तीसरी पंक्ति में 19 गुलाब के पौधे हैं, इत्यादि | यदि उसकी अंतिम पंक्ति में 5 गुलाब के पौधे हैं | इस क्यारी में कुल कितनी पंक्तियाँ हैं ?
Q40. Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?
सुब्बा राव ने 1995 ने 5000 रु के मासिक वेतन पर कार्य आरंभ किया और प्रत्येक वर्ष 200 रु की वेतन वृद्धि प्राप्त की | किस वर्ष में उसका वेतन 7000 रु हो गया ?
Q41. The sum of the 4th and 8th terms of an A.P is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
किसी A.P के चौथे औए 8 वें पदों का योग 24 है तथा छठे और 10 वें पदों का योग 44 है | इस A.P के प्रथम तीन पद ज्ञात कीजिए |
Q42. Which term of the AP : 121, 117, 113, . . ., is its first negative term?
AP : 121, 117, 113, . . . का कौन-सा पद सबसे पहला ऋणात्मक पद होगा ?
Q43. Solve;
(A) Find the value of x for which (8x + 3), (6x – 2) and (2x + 7) are in
sequence.
x का मान ज्ञात कीजिए जिसके लिए (8x + 3), (6x – 2) और (2x + 7) समांतर
श्रेढ़ी में है |
उत्तर :7
उत्तर:
(C) For what value of k 2k-7,k+5 and 3k+2 are the consecutive terms of an A.P.?
k के किस मान के लिए 2k-7,k+5 व 3k+2 समांतर श्रेणी के क्रमागत पद होंगे ?
All Topics Chapter 5. Arithmetic Progressions
5. Arithmetic Progressions-Introduction of Arithmetic Progression Mathematics Class 10 In English-CBSE Notes
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