Class 11 Mathematics Sequence and Series: NCERT Solutions for Question 4

This page offers a step-by-step solution to the specific question NCERT Class 11th Mathematics - Sequence and Series | the 4th nbsp term of a g p is square of its secon Answer from NCERT Class 11th Mathematics, Chapter Sequence and Series.
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, an = arn–1

a4 = ar3 = (–3) r3

a2 = a r1 = (–3) r

According to the given condition,

(–3) r3 = [­(–3) r]2

⇒ –3r3 = 9 r2

⇒ r = –3

a7 = a r 7–1 = a r6 = (–3) (–3)6 = – (3)7 = –2187

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

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