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The third term of a geometric progressio...

The third term of a geometric progression is 4. Then find the product of the first five terms.

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To solve the problem, we need to find the product of the first five terms of a geometric progression (GP) given that the third term is 4. ### Step-by-Step Solution: 1. **Understand the Terms of a GP:** In a geometric progression, the first term is denoted as \( A \) and the common ratio is denoted as \( r \). The terms of the GP can be expressed as: - First term: \( A \) - Second term: \( A \cdot r \) ...
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CENGAGE-PROGRESSION AND SERIES-Examples
  1. The sum of n terms of two arithmetic progressions are in the ratio 5n+...

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  2. If n arithmetic means are inserted between 2 and 38, then the sum of t...

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  3. The third term of a geometric progression is 4. Then find the product ...

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  4. किसी गुणोत्तर श्रेणी का प्रथम पद 1 है | तीसरे एवं पाँचवें पदों का योग...

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  5. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show tha...

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  6. The fourth, seventh, and the last term of a G.P. are 10, 80, and 2560,...

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  7. If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p...

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  8. Does there exist a geometric progression containing 27,8 and 12 as thr...

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  9. In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose...

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  10. For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmeti...

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  11. If (p+q)t h term of a G.P. is aa n d its (p-q)t h term is bw h e r ea ...

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  12. Find four numbers in G.P. whose sum is 85 and product is 4096.

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  13. Three non-zero numbers a ,b ,a n dc are in A.P. Increasing a by 1 or i...

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  14. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/eare in A....

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  15. If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G...

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  16. Insert four G.M.s between 2 and 486.

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  17. If A.M. and G.M. between two numbers is in the ratio m : n then prove ...

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  18. If a be one A.M and G1 and G2 be then geometric means between b and c ...

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  19. Determine the number of terms in G.P. <<an>>,ifa1=3,an=96a n dSn=189.

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  20. if S is the sum , P the product and R the sum of reciprocals of n term...

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