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If the sequence an is A.P., show that a(...

If the sequence `a_n` is A.P., show that `a_(m+n)+a_(m-n)=2a_mdot\ `

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If a_(1), a_(2), . . . , a_(n) is a sequence of non-zero number which are in A.P., show that (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+. . . + (1)/(a_(n)a_(1))= (2)/(a_(1) + a_(n)) [(1)/(a_(1))+(1)/(a_(2))+. . . +(1)/(a_(n))]

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If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

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  2. Evaluate (sqrt(3)-sqrt(2))^6+(sqrt(3)+sqrt(2))^6dot

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  3. If the sequence an is A.P., show that a(m+n)+a(m-n)=2amdot\

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  4. Which term of the A.P. 3,8,13… is 248?

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  5. Which term of the A.P. 84,80,76… is 0?

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  6. Which term of the A.P. 4,9,14… is 254?

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  7. Is 68 as term of the A.P. 7,10,13,…?

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  8. Is 302 a term of the A.P. 3,8,13,…?

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  9. Which term of the sequence 24 ,\ 23 1/4,\ 22 1/2,\ 21 3/4 is the first...

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  10. Which term of the sequence 12+8i ,\ 11+6i ,\ 10+4i ,... is (a) purely ...

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  11. How many terms are there in the A.P. 7,10,13,…43?

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  12. How many terms are there in the A.P. -1,\ -5/6,\ -2/3,-1/2,\ ,(10)/3?

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  13. The first term of an AP. is 5, the common difference is 3 and the last...

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  14. The 6th and 17th terms of an A.P. are 19 and 41 respectively, find t...

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

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  16. The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find...

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  17. In certain A.P. the 24th term is twice the 10th term. Prove that th...

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  18. If the nth term of the A.P. 9,7,5,... is same as the nth term of the A...

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  19. Find the 12th term from the end of the following arithmetic progres...

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  20. Find the 12th term from the end of the following arithmetic progres...

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