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The sum of the 2nd and the 7th terms of ...

The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.

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The correct Answer is:
1, 5, 9, 13,…
`T_(2) + T_(7) = 30 rArr (a+d) + (a+6d) = 30 rArr 2a + 17d = 30. " "…(i)`
`T_(15) = 2T_(8)-1 rArr (a+14d) = 2(a+7d) -1 rArr a = 1.`
Putting a = 1 (i), we get d = 4.
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RS AGGARWAL-ARITHMETIC PROGRESSION-Exercise 5A
  1. The 4th term of an AP is 11. The sum of the 5th and 7th terms of this ...

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  2. The 9th term of an AP is -32 and the sum of its 11th and 13th terms is...

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  3. Determine the general term of an A.P. whose 7t h term is -1 and 16 ...

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  4. If 4 times the 4th term of an AP is equal to 18 times its 18th term th...

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  5. If 10 times the 10 t h term of an A.P. is equal to 15 times the ...

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  6. Find the common difference of an A.P. whose first term is 5 and the su...

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  7. The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term ...

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  8. For what value of n, the nth terms of the arithmetic progressions 63, ...

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  9. The 17th term of AP is 5 more than twice its 8th term. If the 11th ter...

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  10. The 24th term of an AP is twice its 10th term. Show that its 72nd term...

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  11. The 19th term of an AP is equal to 3 times its 6th term. If its 9th te...

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  12. In an AP, the pth term is q and ( p +q) term is 0. Then, prove that i...

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  13. The first and the last terms of an A.P. are a\ a n d\ l respectively. ...

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  14. Find how many two-digit numbers are divisible by 6.

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  15. How many two -digit numbers are divisible by 3?

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  16. How many two-digit numbers are divisible by 9?

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  17. Find the number of natural numbers between 101 and 999 which are di...

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  18. In a flower bed, there are 43 rose plants in the first row, 41 in the ...

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  19. A sum of Rs. 2800 is to be used to award four prizes. If each prize af...

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  20. Find how many integers between 200 and 500 are divisible by 8.

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