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If a, b, c are in A.P., b, c, d are in G...

If a, b, c are in A.P., b, c, d are in G.P. and `1/c ,""1/d ,""1/e` are in A.P. prove that a, c, e are in G.P.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. The sum of three numbers in GP. is 56. If we subtract 1, 7, 21 from ...

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  2. Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+...

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  3. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are ...

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  4. Find the sum sum(r=0)^n^(n+r)Cr .

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  5. Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1...

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  6. Write the first five terms of the following sequence and obtain the ...

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  7. Prove that the sum to n terms of the series 11+103+1005+ i s(10/9)(10^...

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  8. If a(n+1)=1/(1-an) for n>=1 and a3=a1. then find the value of (a200...

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  9. Determine the number of terms in a G.P., if a1=3,an=96 ,a n dSn=189.

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  10. Let {an}(ngeq1) be a sequence such that a1=1,a n d3a(n+1)-3an=1 for a...

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  11. Let S be the sum, P the product, and R the sum of reciprocals of n ter...

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  12. If the pth term of an A.P. is q and the qth term is p , then find its ...

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  13. Find the product of three geometric means between 4 and 1/4.

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  14. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

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  15. Insert four G.M.’s between 2 and 486.

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  16. Find the sum 1^2+(1^2+2^2)+(1^2+2^2+3^2)+ up to 22nd term.

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  17. If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G...

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  18. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

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  19. The sum of infinite number of terms in G.P. is 20 and the sum of their...

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  20. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) ...

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