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We are given an A.P. with 1st term a and...

We are given an A.P. with 1st term a and common difference d.
If each of the terms is multiplied by the same number c, is the resulting progression also an A.P. ? If so, find its common difference.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Find four terms in A.P. whose sum is 20 and the sum of whose squares i...

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

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

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

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  6. If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)...

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  7. If 1/a,1/b,1/c are in A.P., prove that : (b + c)/a, (c + a)/b, (a + ...

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  8. If 1/a,1/b,1/c are in A.P., prove that : a(b + c), b(c + a), c(a + b...

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  9. If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove ...

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  10. If a^(2),b^(2),c^(2) are in A.P. Prove that (a)/(b+c),(b)/(c+a),(c)/(a...

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  11. If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,...

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  12. Find 'r' and write the fourth term of the following progressions : ...

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  13. Find 'r' and write the next four terms of the following progressions :...

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  14. Find the 20th and nth terms of the G.P. 5/2,5/4,5/8,.....

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  15. Find the indicated term(s) of the following G.P.'s : 12, 8, 16/3, ……...

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  16. Which term of the geometric sequences : 2, 8, 32, is 131072 ?

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  17. Which term of the following sequence:- sqrt3,3,3sqrt3,....is 729?

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  18. Which term of the following sequence:- 1/3,1/9,1/27,.....is 1/19683 ?

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  19. For what values of x, the numbers -2/7,x, -7/2 are in G.P.?

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  20. In a G.P., the third term is 24 and the 6th term is 192. Find the 10th...

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