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Show `(m+n)th and (m-n)t h` terms of an A.P. is equal to twice the mth terms.

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32. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A.P. is equal to twice the m^(th) term

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If 10 times the 10 t h term of an A.P. is equal to 15 times the 15 t h term, show that 25 t h term of the A.P. is zero.

If m times the m^(t h) term of an A.P. is equal to n times its n^(t h) term, show that the (m+n)^(t h) term of the A.P. is zero.

If m times the m^(t h) term of an A.P. is equal to n times its n^(t h) term, show that the (m+n)^(t h) term of the A.P. is zero.

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. In an A.P. of 99 terms, the sum of all the odd-numbered terms is 2550....

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  2. Divide 32 into four parts which are in A.P. such that the ratio of the...

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  3. Show (m+n)th and (m-n)t h terms of an A.P. is equal to twice the mth ...

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  4. If the sum of three consecutive numbers in A.P., is 24 and their pr...

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  5. Prove that the sum of n number of terms of two different A.P. s can be...

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  6. In an A.P. if S1=T1+T2+T3+.....+Tn (n is odd)S2=T2+T4+T6+.........+T(n...

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  7. If the sum of the series 2, 5, 8, 11, ... is 60100, then find the valu...

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  8. The digits of a positive integer, having three digits, are in A.P. and...

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  9. If eleven A.M. ‘s are inserted between 28 and 10, then find the number...

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  10. Between 1 and 31, m numbers have been inserted in such a way that t...

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  11. Find the sum of first 24 terms of the A.P. a1,a2, a3 ......., if it i...

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  12. If the arithmetic progression whose common difference is nonzero the ...

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  13. The sum of n terms of two arithmetic progressions are in the ratio 5n+...

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  14. If the first two terms of as H.P. are 2/5 and 12/13, respectively. The...

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  15. Insert five arithmetic means  between 8 and 26. or Insert five numbers...

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  16. If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove ...

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  17. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  18. If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H...

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  19. Find the sum of all three-digit natural numbers, which are divisible b...

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  20. If a ,b ,c ,and d are in H.P., then find the value of (a^(-2)-d^-2)/(b...

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