# Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.

Given: S2 = —4 and a5 = 4 × a3

The Sum of terms in G.P. is given by: S2 = = —4 = —4

a(1+r) = —4 –1

Here,

a5 = 4 × a3

ar4 = 4 × ar2 ( nth term of the G.P is arn-1)

r2 = 4

r = 2

r = +2 or –2

Case 1: r = +2

From eq –1

a(1+r) = —4

a(1+2 ) = —4

a = G.P : Case 2: r = –2

From eq –1

a(1+r) = —4

a(1+(–2) ) = —4

a = = 4

G.P : 4 , –8, 16, –32,…….

The possible G.P ‘s are or 4 , –8, 16, –32,…….

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