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Insert Two Numbers Between 3 and 81 So that the Resulting Sequence is Geometric Progression - Mathematics

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

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Solution

Let G1 and G2 be two numbers between 3 and 81 such that the series, 3, G1G2, 81, forms a G.P.

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

∴81 = (3) (r)3

⇒ r3 = 27

∴ r = 3 (Taking real roots only)

For r = 3,

G1 = ar = (3) (3) = 9

G2 = ar2 = (3) (3)2 = 27

Thus, the required two numbers are 9 and 27

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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 9 Sequences and Series
Q 26 | Page 193
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