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If a, b, c are in A.P., prove that : a...

If a, b, c are in A.P., prove that :
`a^3+4b^3+c^3=3b (a^2+c^2)`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. n arithmetic means are inserted between 3 and 17 such that ratio of fi...

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  2. If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac).

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  3. If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2).

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  4. Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the ge...

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  5. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find ...

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  6. Between 1 and 31, n A.M's have been inserted in sucha a way that the r...

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  7. Find three numbers in A.P. : whose sum is 21 and product is 315.

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  8. Find three numbers in A.P. : whose sum is 24 and Product is 440.

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  9. The sum of the first three terms of an A.P. is 36 while their product ...

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  10. The sum of three Consecutive terms of an A.P. is 15 and sum of their S...

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  11. The sum of three consecutive terms of an A.P. is 9 and the sum of thei...

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  12. Split 69 into three parts in A.P. such that the product of the two sma...

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  13. Solve the equation : 1+6+11+ 16+.....+x= 148

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  14. Solve the equation : 2+5+8+ 11+...... +x = 345.

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  15. The sum of four numbers in A.P. is 4 and their product is 385. Find th...

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  16. Find four terms in A.P. whose sum is 20 and the sum of whose squares i...

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  17. We are given an A.P. with 1st term a and common difference d. If ea...

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  18. We are given an A.P. with 1st term a and common difference d. If eac...

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  19. If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

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  20. If a, b, c are in A.P., prove that : 1/(sqrtb+sqrtc), 1/(sqrtc+sqrta...

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