Q. 34.5( 2 Votes )

If the 4th and 7th terms of a G.P. are 54 and 1458 respectively, find the G.P.

Answer :

a4 = 54 and a7 = 1458

an = a1rn-1 (n = no. of term, a1 = first term of G.P, r = common ratio)


a4 = a1r3


54 = a1r3 ………(1)


Also, a7 = a1r6


1458 = a1r6 ………(2)


Dividing equation (1) & (2), we get-



r3 = 27


r3 = 33


r = 3


Now, putting value of r in equation (1), we get-


54 = a133



a1 = 2


Now, G.P will be-


a1 , a1r ,a1r2, a1r3,………


2, 2 × 3, 2 × 32, 2 × 3…


2, 6, 18, 54,… is the G.P.


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