1.

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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