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If the first and the nth terms of a GP a...

If the first and the nth terms of a GP are a and b respectively and if P is the product of the first n terms, then `P^(2)` is equal to

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To solve the problem, we need to find \( P^2 \) where \( P \) is the product of the first \( n \) terms of a geometric progression (GP) with the first term \( a \) and the \( n \)th term \( b \). ### Step-by-Step Solution: 1. **Identify the first and nth terms of the GP:** - The first term \( a_1 = a \). - The nth term \( a_n = ar^{n-1} = b \), where \( r \) is the common ratio. ...
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NCERT ENGLISH-SEQUENCES AND SERIES-EXERCISE 9.3
  1. If the first and the nth terms of a GP are a and b respectively and if...

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  2. Find four numbers forming a geometric progression in which the third ...

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  3. Show that the products of the corresponding terms of the sequences a,...

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  4. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n)may be the geo...

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  5. Insert two number between 3 and 81 so that the resulting sequence is ...

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  6. If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b...

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  7. The number of bacteria in a certain culture doubles every hour. If th...

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  8. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

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  9. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respect...

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  10. If A and G be A.M. and GM., respectively between two positive numbers...

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

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  12. If the p^(t h),q^(t h)and r^(t h)terms of a GP are a, b and c, respec...

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  13. Show that the ratio of the sum of first n terms of a G.P. to the su...

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  14. Find a G.P. for which sum of the first two terms is - 4 and the fift...

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  15. If the 4^(t h), 10^(t h)and 16^(t h)terms of a G.P. are x, y and z, r...

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  16. The sum of first three terms of a G.P. is 16 and the sum of the next ...

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  17. Given a G.P. with a = 729 and 7^(t h)term 64, determine S7.

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  18. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  19. How many terms of G.P. 3,3^2,3^3,dotdotdotare needed to give the sum 1...

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  20. Find the sum to indicated number of terms in each of the geometric pr...

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