# The 4th term of a G.P. is square of its second term, and the first term is – 3. Determine its 7th term.

Given: a4 = (a2)2 and a = –3

We know that in G.P an = arn-1

a2 = (–3) × r2-1 = –3r( a = –3)

Similarly,

a4 = –3r3

–3r3 = (-3r)2 ( a4 = (a2)2 )

–3r3 = 9r2

r = –3

r = –3

Now,

a7 = ar7-1

a7 = (–3)( –3)6 ( a = –3 and r = –3)

a7 = ( –3)7 = – 2187.

a7 = – 2187

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