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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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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.

If the sum of the first m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, prove that, (m+n)((1)/(m)-(1)/(p)) = (m+p)((1)/(m) - (1)/(n))

The sum of first P terms of an A.P. is equal to the sum of its first Q terms. Show that the sum of its first (P+Q) terms is zero.

If the mth and nth terms of a H.P. are n and m respectively, then its mnth term will be-

The ratio of the 11th and 14th terms of an A.P. is 7:9, find the ratio of the 10th term to 3rd term of the series.

if the Pth term of an A.P. is q and qth term is P.Then show that the nth term is p+q-n

Find the 31st term of an A.P. whose 11th term is 38 and 6th term is 73.

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

The sum to n terms of an A.P. is n^(2) . Find the common difference.

CENGAGE PUBLICATION-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 a, b a n d c are in A.P., a x ,b y ,a n dc z in G.P. and x,y,z 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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