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Find the sum of indicated terms of each ...

Find the sum of indicated terms of each of the following geometric progressions :
(i) 2, 4, 8, 16 ,…, 20 terms
(ii) ` 1 , (-2)/(3) , (4)/(9) , (-8)/(27) ,…, 10 ` terms

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To solve the problem of finding the sum of indicated terms of the given geometric progressions, we will break it down into two parts. ### Part (i): Sum of the first 20 terms of the geometric progression 2, 4, 8, 16, ... 1. **Identify the first term (a) and common ratio (r)**: - The first term \( a = 2 \) - The common ratio \( r = \frac{4}{2} = 2 \) ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
  1. Find the sum of indicated number of terms of each of the following G.P...

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

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  3. Find the sum of indicated terms of each of the following geometric pro...

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

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

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  6. A bag contains a total of 20 books on physics and mathematics, Any po...

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  7. Find the sum to infinity of the following G.P. (i) 1, (1)/(3) , (1)/...

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  8. Find the sum of the following series , (i) 0.5 + 0.05 + 0.005 + 0...

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

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

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

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

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

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

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

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

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

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

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  19. Insert four number between 6 and 192 so that the resulting sequence is...

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  20. Insert six G.M. ' s between (8)/(27) and (-81)/(16) .

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