Question

Given u1 = 56 and un = 0.7un-1, find S12. Round to the nearest hundredth A) 181.39 B) 184.08 C) 185.32 D) 186.66

Answer 1

184.08

Explanation:

`u_(1),u_(2),u_(3).....u_(n)` form a sequence exhibiting the following property :

`u_(1)=56;u_(n)=0.7u_(n-1)`

On rewriting,
`(u_(n))/(u_(n-1))=0.7` ⇒ Ratio of consecutive terms is a constant. Hence, the sequence is a Geometric Progression.

The ratio
`0.7` is the common ratio
`r`. First term =
`a=`
`u_(1)=56`.

Sum of
`n` terms of a Geometric progression is given by

`S_(n)=a*(1-r^(n))/(1-r)` when
`r<1`.

`S_(12)=56*((1-(0.7)^(12))/(1-0.7))=56*(0.986)/(0.3)=184.083`

∴
`S_(12)` to the nearest hundreth is 184.08