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The 4th term of a G. P. is 16 and the 7th term is 128. Find the first term and common ratio of the series. |
Answer» Let a and r be the first term and common ratio of given G.P. ∴ a4= 16 ⇒ ar3 = 16 and a7 = 128 ⇒ a6 = 128 Dividing (ii) and (i), we obtain ar6/ar3 = 128/16 a3 = 3 a3 = 23 a = 2 ⇒ From (i), we have 2(r3) = 16 r3 = 8 r3 = 23 ⇒ r = 2 Hence, the first term and common ratio of the given series is 2 and 2. |
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