Question

7. A geometric series consists of four terms and has a positive common ratio. The sum of the first two terms is 9 and sum of the last two terms is 36. Find the series.

Answer 1

Let a , ar , ar² , ar³ are in GP
sum of first two terms = (a + ar) = 9
a(1 + r) = 9----(1)
sum of last two terms = (ar² + ar³) = 36
ar²(1 + r) = 36 ----(2)

dividing equation (2) by (1)
ar² (1 + r)/a(1 + r) = 36/9
r² = 4 ⇒r = ± 2
but a/c to question, r is positive so, r = 2
Now, put r = 2 In equation (1)
∴ a = 3
So, series are 3 , 6 , 12 , 24

Answer 2

Let a , ar , ar² , ar³ are in GP

sum of first two terms = (a + ar) = 9
a(1 + r) = 9----( 1 )

sum of last two terms = (ar² + ar³) = 36
ar²(1 + r) = 36 -------- ( 2 )


dividing equation (2) by (1)
ar² (1 + r)/a(1 + r) = 36/9

r² = 4

r = ± 2

but in question , r is positive so, r = 2

Now, [ put r = 2 In equation ( 1 )]

a (1 + 2) = 9

3a = 9

a = 3


Hence, series are 3 , 6 , 12 , 24


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