NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 60

Total: 106

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

Solution:

Let G1,G2 be two numbers between 3 and 81 such that 3, G1,G2 , 81 is a G.P.
Since a4 = 81 ⇒ ar3 = 81 ⇒ 3r3 = 81 (Since a = 3) ⇒ r3 = 27 ⇒ r = 3
Since a2 = G1 ⇒ G1 = ar = 3 × 3 = 9
Since a3 = G2 ⇒ G2 = ar2 = 3 × (3)2 = 27
Hence, we can insert 9, 27 between 3 and 81 so that the resulting sequence is in G.P.

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