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 numbers
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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 number is 13 and geometric mean is 12 , then find that numbers
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Problem : 9 [ Geometric Progression ]       Solve this type of problem
9. Two numbers are in the ratio 9 : 16 and difference of arithmetic mean and geometric mean is 1 , then find that numbers
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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 * (2^2 - 3^2) + 2 * (3^2 - 4^2) + 3 * (4^2 - 5^2) + ... n` terms `= n/6 (n + 1) (4n + 11)`
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Problem : 14 [ Geometric Progression ]       Solve this type of problem
14. `1 + x^4 + 3^2 + 4 + x^6 + 6^2 + 7 + x^8 + 9^2 + ... 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, `1^2 * n + 2^2 * (n - 1) + 3^2 * (n - 2) + ... + n^2 * 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 * 2^2 + 3 * 5^2 + 5 * 8^2 + ... n` terms `= n/2 (9n^3 + 4n^2 - 4n - 1)`
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Problem : 18 [ Geometric Progression ]       Solve this type of problem
18. Prove that `1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ... 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 (2n^2 + 3n + 7)`
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Problem : 20 [ Geometric Progression ]       Solve this type of problem
20. Prove that `sum [ sum (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 ( 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` , ( 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, ( Find `a^2 + b^2 + ... n` terms, where a = 1 , b = 2 and n = 10 . )
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