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The sum of the first 7 terms of an AP is...

The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in the ratio 1:5, find the AP.

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The correct Answer is:
2, 10, 18, 26,…
`(7)/(2)(2a + 6d) = 182 rArr a + 3d = 26. " "…(i)`
`(a+3d)/(a+16d) = (1)/(5) rArr 5a+15d =a + 16d rArr 4a-d = 0 " "…(ii)`
Solve (i) and (ii), we get a = 2 and d = 8.
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RS AGGARWAL-ARITHMETIC PROGRESSION-Exercise 5C
  1. In an A.P., the first term is 22, n t h term is -11 and the sum ...

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  2. The 12th term of an AP is -13 and the sum of its first four terms is 2...

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  3. The sum of the first 7 terms of an AP is 182. If its 4th and 17th term...

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  4. The sum of the first 9 terms of an AP is 81 and that of its first 20 t...

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  5. If the sum of first 7 terms of an AP is 49 and that of 17 terms is ...

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  6. Two Aps have the same common difference. If the first terms of these A...

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  7. In an AP, the sum of first ten terms is -150 and the sum of its next t...

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  8. The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 ...

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  9. The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41...

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  10. (i) An AP 5, 12, 19,.. has 50 terms. Find its last term. Hence, find t...

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  11. The sum of n terms of two arithmetic progressions are in the ratio (3n...

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  12. The sum of the 4th and the 8 the terms of an AP is 24 and the sum of i...

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  13. The sum of first m terms of an AP is (4m^2-m) If its nth term is 107, ...

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  14. The sum of first q terms of an AP is (63q -3q^(2)). If its pth term is...

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  15. Add number of terms of the "A*P*-12-9,-6,.....If 1 is added to each te...

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  16. Sum of the first 14 terms of an AP is 1505 and its first term is 10. F...

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  17. Find the sum of first 51 terms of an AP whose second and third terms ...

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  18. In a school, students decided to plant trees in and around the school ...

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  19. In a potato race, a bucket is placed at the starting point, which is 5...

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  20. There are 25 trees at equal distances of 5 metres n a line with a well...

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