Question

Find the sun of the first 8 terms of the following series, to the nearest integer. 48,60,75

Answer 1

S₈ ≈ 952

Explanation:

48 , 60 , 75

there is a common ratio between consecutive terms in the sequence

`(60)/(48)` =
`(75)/(60)` =
`(5)/(4)` = 1.25

this indicates the sequence is geometric with sum to n terms

`S_(n)` =
`(a_(1)(r^(n)-1) )/(r-1)`

where a₁ is the first term and r the common ratio

here a₁ = 48 and r = 1.25 , then

S₈ =
`(48(1.25^(8)-1 ))/(1.25-1)`

=
`(48(5.960464478-1))/(1.25-1)`

=
`(48(4.960464478)/(0.25)`

= 192 × 4.960464478

= 952.4091797

≈ 952 ( to the nearest integer )