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Find the sum of indicated number of term...

Find the sum of indicated number of terms of each of the following G.P.
(i) 2, 4, 8, …, to 10 terms
(ii) ` sqrt(2) , 2 , sqrt(8),..` to 12 terms

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To find the sum of the indicated number of terms of each of the given geometric progressions (G.P.), we will use the formula for the sum of the first n terms of a G.P.: \[ S_n = \frac{a(r^n - 1)}{r - 1} \] where: - \( S_n \) is the sum of the first n terms, ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
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  2. The sum of four numbers in G.P is 60 and the arithmetic mean of the ...

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  3. Find the sum of indicated number of terms of each of the following G.P...

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  4. Find the sum of the following series : (1)/(4) + (1)/(2) + 1 + … to...

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  6. Find the sum to n terms (i) 9 + 99 + 999 + … (ii) 0.2 + 0.22...

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  7. How many terms of the series 1+2+2^2+….. must be taken to make 511?

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  11. Prove that (9^(1/3).9^(1/9).9^(1/27)............oo)=3

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  12. Show that 9^(1/(4)).9^(1/(8)).9^(1/(16).) . .."to" oo = 3

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  13. The sum of an infinite G.P. . Is 6 and its first term is 2 . Find the ...

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  14. If the common ratio is -4/5 and the sum of infinite terms in a G.P is ...

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  15. Represent the following as rational numbers : (i) 0.bar(8)5 " " (...

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  16. Represent the following as rational numbers : (i) 0.bar15 " " (ii)...

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  17. If a, b, c , d are in G.P. , then shown that (i) (a + b)^(2) , (b ...

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  18. If a, b, c are in G.P. , then show that (i) (a^(2) - b^(2))(b^(2)...

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  19. Find the G.M. between the numbers. (i) 6 and 216 " " (ii...

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  20. Find the G.P. between the numbers . 1 and (4)/(25) " " ...

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