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The sum of the 4th and the 8 the terms o...

The sum of the 4th and the 8 the terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find its first term.

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The correct Answer is:
`S_(10) = 95`
`T_(4) + T_(8) = 24 rArr (a+3d) + (a+7d) = 24 rArr a +5d = 12. " "…(i)`
`T_(6) + T_(10) = 44 rArr (a+5d) + (a+9d) = 44 rArr a+7d = 22. " "…(ii)`
Solve (i) and (ii), we get a = -13 and d = 5.
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RS AGGARWAL-ARITHMETIC PROGRESSION-Exercise 5C
  1. Two Aps have the same common difference. If the first terms of these A...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. A sum of Rs 700 is to be used to give seven cash prizes to students...

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  17. A man saved ₹ 33000 in 10 months. In each month after the first, he sa...

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  18. A man arranges to pay a debt of Rs 3600 in 40 monthly installments whi...

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  19. A contract on construction job specifies a penalty for delay of com...

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  20. A child puts one five-rupee coin of her saving in the piggy bank on th...

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