The third term of a G.P. is greater than its first term by 9 whereas its second term is greater than the fourth term by 18. Find the G.P.

Let first term be a and common ratio be r. By formula, ⇒ a n = ar n - 1 Given, The third term of a G.P. is greater than its first term by 9. ∴ a 3 - a = 9 ⇒ ar 3 - 1 - a = 9 ⇒ ar 2 - a = 9 ⇒ a(r 2 - 1) = 9 ⇒ a = .......(1) Given, Second term is greater than the fourth term by 18. ∴ a 2 - a 4 = 18 ⇒ ar 2 - 1 - ar 4 - 1 = 18 ⇒ ar - ar 3 = 18 ⇒ ar(1 - r 2 ) = 18 Substituting value of a from equation (1) in above equation, we get : Substituting value of r in equation (1), we get : G.P. = a, ar, ar 2 , ar 3 , ....... = 3, 3 × -2, 3 × (-2) 2 , 3 × (-2) 3 , ....... = 3, -6, 3 × 4, 3 × -8, ........ = 3, -6, 12, -24, ........ Hence, required G.P. = 3, -6, 12, -24, ........

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The 5^th and the 8^th terms of a G.P. are 32 and 256 respectively. Find its first term and the common ratio.

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x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

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The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

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Mathematics

The third term of a G.P. is greater than its first term by 9 whereas its second term is greater than the fourth term by 18. Find the G.P.

AP GP

Related Questions

The 5^th and the 8^th terms of a G.P. are 32 and 256 respectively. Find its first term and the common ratio.

x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

Mathematics

The third term of a G.P. is greater than its first term by 9 whereas its second term is greater than the fourth term by 18. Find the G.P.

AP GP

Related Questions

The 5th and the 8th terms of a G.P. are 32 and 256 respectively. Find its first term and the common ratio.

x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

The 5^th and the 8^th terms of a G.P. are 32 and 256 respectively. Find its first term and the common ratio.