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If the common ratio is -4/5 and the sum ...

If the common ratio is `-4/5` and the sum of infinite terms in a G.P is `(80)/9` then find the first term.

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To solve the problem, we need to find the first term of a geometric progression (G.P.) given the common ratio and the sum of the infinite terms. ### Step-by-step Solution: 1. **Identify the Given Values**: - Common ratio \( r = -\frac{4}{5} \) - Sum of infinite terms \( S = \frac{80}{9} \) ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
  1. Show that 9^(1/(4)).9^(1/(8)).9^(1/(16).) . .."to" oo = 3

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

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

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

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

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

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

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

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

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

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

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  12. If one G.M., G and two A.M's p and q be inserted between two given num...

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  13. The sum of two numbers is 6 times their geometric means, show that nu...

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  14. If the A.M. between two positive numbers exceeds their G.M. by 2 and t...

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  15. If G(1) is the first of n G.M. s between positive numbers a and b ,...

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  16. Find the 15^(th) term of the series 3 - 6 +9 - 12 + …

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  17. Find the r^(th) term of the series (2)/(4) + (4)/(4^(2)) + (6)/(4...

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  18. Find the following sums : (i) 1 + 2 + 3 + …+ 30 (ii) 1^(2) + 2^...

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  19. Find the following sums : (i) 5 + 6 + 7 +…+ 100 (ii) 15^(2) + 16...

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  20. Find the sum of n terms of the series whose nth terms is (i) n(n-1)...

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