The 4th Term of a G.P. is Square of Its Second Term, and the First Term is –3. Determine Its 7thterm. - CBSE (Arts) Class 11 - Mathematics
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The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.
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
⇒ 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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Solution The 4th Term of a G.P. is Square of Its Second Term, and the First Term is –3. Determine Its 7thterm. Concept: Geometric Progression (G. P.).