Question 4

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

Answer

Let *a* be the first term and *r* be the common ratio of the G.P.

∴ *a* = –3

It is known that, *a*n = *ar**n*–1

∴*a*_{4} = *ar*^{3} = (–3) *r*^{3}

*a*_{2} = *a r*^{1} = (–3) *r*

According to the given condition,

(–3) *r*^{3} = [(–3) *r*]^{2}

⇒ –3*r*^{3} = 9 *r*^{2}

⇒ *r* = –3

*a*_{7} = *a* *r* ^{7}–1 = *a* *r*^{6} = (–3) (–3)6 = – (3)7 = –2187

Thus, the seventh term of the G.P. is –2187.

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- NCERT Chapter