Question

The 1st, 5th and 10th terms of a linear sequence of a Geometric Progression. If the sum of the 2nd and 8th term is 30,find the first term

Answer 1

In GP,

$1st = a$

$2nd =ar^2$

$5 th =ar^4$

$8 th =ar^7$

10th term $=ar^9$

Common Ratio (r) $=ar^4/a= ar^9/ar^4$

Common Ratio (r) $=r^4= r^5$

Common Ratio (r) = 1

2nd and 8th term = 30 =$ar+ ar^7=30$

$a(1)+ a(1)^7=30$

$a+a=30$

$2a = 30$

$a = 15$

Therefore, the first term is 15