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Find the least value of n for which the...

Find the least value of `n` for which the sum `1+3+3^2+ ton` terms is greater than 7000.

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To find the least value of \( n \) for which the sum \( 1 + 3 + 3^2 + \ldots + 3^{n-1} \) is greater than 7000, we can follow these steps: ### Step 1: Identify the series The given series is a geometric progression (GP) where: - The first term \( a = 1 \) - The common ratio \( r = 3 \) ### Step 2: Write the formula for the sum of the first \( n \) terms of a GP ...
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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If S1, S2, ,Sn are the sum of n term of n G.P., whose first term is 1...

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  2. If S1, S2, S3 be respectively the sums of n ,2n ,3n terms of a G.P., t...

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  3. Find the least value of n for which the sum 1+3+3^2+ ton terms is gr...

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  4. Prove that the sum of n terms of the series: 11+103+1005+ i s(10)/9(10...

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  5. How many terms of the sequence sqrt(3),3,3sqrt(3) must be taken to mak...

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  6. How many terms of the G.P. 3,3//2,3//4, be taken together to make (30...

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  7. If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^...

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  8. If a ,b ,c ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

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  9. If a ,b ,c are in G.P., then prove that loga^n ,logb^n ,logc^n are in ...

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  10. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

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  11. If S denotes the sum of an infinite G.P. adn S1 denotes the sum of the...

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  12. The sum of first two terms of an infinite G.P. is 5 and each term is ...

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  13. One side of an equilateral triangle is 18 cm. The mid-point of its ...

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  14. If Sp denotes the sum of the series 1+r^p+r^(2p)+... tooo and S(p') t...

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  15. If each term of an infinite G.P. is twice the sum of the terms foll...

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  16. If |x|<1a n d|y|<1, find the sum of infinity of the following series:...

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  17. Find the sum of n terms of the sequence (x+1/x)^2,(x^2+1/(x^2))^2,(x^3...

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  18. Find the sum to n terms of the sequence given by an=2^n,n in Ndot

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  19. Sum the series : x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton terms.

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  20. Find the sum of the following series : 0. 7+0. 77+0. 777+ ton term...

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