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Geometric Progression 
 
Problem : 1 [ Geometric Progression ]       Solve this type of problem
1. For given geometric progression series 3,6,12,24,48 ,... find 10 th term and addition of first 10 th terms.
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Problem : 2 [ Geometric Progression ]       Solve this type of problem
2. For given geometric progression series 3,6,12,24,48 ,... then find n such that S(n) = 3069 .
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Problem : 3 [ Geometric Progression ]       Solve this type of problem
3. For given geometric progression series 3,6,12,24,48 ,... then find n such that f(n) = 1536 .
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Problem : 4 [ Geometric Progression ]       Solve this type of problem
4. For geometric progression f( 1 ) = 2 , f( 4 ) = 54 then find f( 3 ) and S( 3 ).
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Problem : 5 [ Geometric Progression ]       Solve this type of problem
5. For geometric progression f( 1 ) = 2 , f( 4 ) = 54 , then find n such that f(n) = 18 .
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Problem : 6 [ Geometric Progression ]       Solve this type of problem
6. For geometric progression addition of 3 terms is 26 and their multiplication is 216 , then that nos.
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Problem : 7 [ Geometric Progression ]       Solve this type of problem
7. For geometric progression multiplication of 5 terms is 1 and 5 th term is 81 times then the 1 th term.
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Problem : 8 [ Geometric Progression ]       Solve this type of problem
8. Arithmetic mean of two no is 13 and geometric mean is 12 , then find that nos.
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Problem : 9 [ Geometric Progression ]       Solve this type of problem
9. Two nos are in the ratio 9 : 16 and difference of arithmetic mean and geometric mean is 1 , then find that nos.
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Problem : 10 [ Geometric Progression ]       Solve this type of problem
10. Find 6 arithmetic mean between 3 and 24 .
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Problem : 11 [ Geometric Progression ]       Solve this type of problem
11. Find 3 geometric mean between 1 and 256 .
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Problem : 12 [ Geometric Progression ]       Solve this type of problem
12. Prove that 1 + (1 + 2) + (1 + 2 + 3) + ... n terms = n/6 (n + 1) (n + 2)
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Problem : 13 [ Geometric Progression ]       Solve this type of problem
13. Prove that 1 × (22 - 32) + 2 × (32 - 42) + 3 × (42 - 52) + ... n terms = n/6 (n + 1) (4n + 11)
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Problem : 14 [ Geometric Progression ]       Solve this type of problem
14. 1 + x4 + 32 + 4  + x6 + 62 + 7  + x8 + 92 + ... 3n terms
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Problem : 15 [ Geometric Progression ]       Solve this type of problem
15. 1 + (1 + 3) + (1 + 3 + 5) + ... n terms
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Problem : 16 [ Geometric Progression ]       Solve this type of problem
16. Prove that for all n belongs to N, 12 × n + 22 (n - 1) + 32 (n - 2) + ... + n2 × 1 = n/12 (n + 1)2 (n + 2)
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Problem : 17 [ Geometric Progression ]       Solve this type of problem
17. Prove that 1 × 22 + 3 × 52 + 5 × 82 + ... n terms = n/2 (9n3 + 4n2 - 4n -1)
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Problem : 18 [ Geometric Progression ]       Solve this type of problem
18. Prove that 12 + (12 + 22) + (12 + 22 + 32) + ... n terms = n/12 (n + 1)2 (n + 2)
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Problem : 19 [ Geometric Progression ]       Solve this type of problem
19. Prove that 2 + 5 + 10 + 17 + ... n terms =n/6 (2n2 + 3n + 7)
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Problem : 20 [ Geometric Progression ]       Solve this type of problem
20. Prove that S [ S (2n -3) ] =n/6 (n + 1)(2n - 5)
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Problem : 21 [ Geometric Progression ]       Solve this type of problem
21. For geometric progression, find 1 + 1/sqrt(2) + 1/2 + 1/2*sqrt(2) + ... 10 terms ( 21. For geometric progression, find 1 + 1/sqrt(x) + 1/x + 1/x*sqrt(x) + ... n terms where x = 2 and n = 10 . )
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Problem : 22 [ Geometric Progression ]       Solve this type of problem
22. Find 1^2 + 2^2 + ...+ 10^2 , ( 22. Find a^2 + b^2 + ...+ n^2 , where a = 1 , b = 2 and n = 10 . )
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Problem : 23 [ Geometric Progression ]       Solve this type of problem
23. Find 1^2 + 2^2 + ... 10 terms, ( 23. Find a^2 + b^2 + ... n terms, where a = 1 , b = 2 and n = 10 . )
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