Question

Find the sum of the first ten terms

using the formula:
a(1-rn)
1,3/2,9/4,27/8,81/16

Answer 1

1

Explanation:

T1(a) = 1

T2(ar) = 3/2

T3(ar²) = 9/4

T4(ar³) =27/8

T5(ar⁴) = 81/16

lets look for r

by using the formula

`(t \\ 2)/(t1) = (t3)/(t2) = (t4)/(t3) = r`

let us use T2/T1

`( \\ ar)/(a) = (3)/(2) / 1 = (3)/(2) * (1)/(1) = (3)/(2)`

`r = ( \\ 3)/(2)`

since r > 1 we will use this formula

`s10 = (a \\ ( r - 1))/(r - 1)`

by substituting

`s10 = ( \\ 1( (3)/(2) - 1))/( (3)/(2) - 1 )`

`= ( \\ (3)/(2) - 1)/( (3)/(2) - 1 )`

`= ( \\ (1)/(2) )/( (1)/(2) )`

`(1)/(2 \\ ) / (1)/(2)`

`(1)/(2 \\ ) * (2)/(1)`

`(2)/(2 \\ ) = 1`

therefore the sum of first ten term of the sequence is 1