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If the nth term of a series be (2.3^(n-1...

If the nth term of a series be `(2.3^(n-1) + 1)`, find the sum of first r terms of the series.

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The correct Answer is:
`3^(r ) + r-1`
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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Short Answer Type Questions)
  1. Find the sum to n terms of the followig series : 1+3+7+15+31+…

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  2. Find the sum to n terms of the followig series : 3+7+14+27+52+…

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  3. If the nth term of a series be (2.3^(n-1) + 1), find the sum of first ...

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  4. If a, b, c, be respectively the pth, qth and rth terms of a G.P., prov...

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  5. If a, b, c and d are in G.P., show that, (a-b)^(2), (b-c)^(2), (c-d)...

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  6. If a, b, c and d are in G.P., show that, a^(2) + b^(2), b^(2) + c^(...

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  7. If a, b, c and d are in G.P., show that, a^(2)+b^(2)+c^(2), ab+bc+c...

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  8. If a, b, c and d are in G.P., show that, (b-c)^(2) + (c-a)^(2)+ (d-b...

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  9. If three numbers a, b, c satisfy the relation (a^(2) + b^(2)) (b^(2) +...

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  10. If a, b, c are in geometric progression, then show that, (a^(2) + ab...

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  11. A boy saves 1 paisa the first day, 2 paise the second day, 4 paise the...

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  12. Shri A. K. Roy borrows Rs. 6000 to repay the amount with interest of R...

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  13. A man borrows Rs. 19682 without interest and agrees to repay the money...

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  14. The A.M. of two numbers is 15 and their G.M. is 12. Find the numbers.

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  15. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  16. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

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  17. If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^...

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  18. The sum of three numbers in G.P. is 70. If each of the two extremes be...

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  19. Let t(r) be the rth term of an A.P. If t(2), t(8) and t(32) are in G.P...

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  20. If p, q, r be in arithmetic progression, then show that the pth, qth a...

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