Question

Question #6a3be

Answer 1

`512`

Here are two methods of solution, one algebraic and one arithmetical.

Algebraic

The `k` th term is `ar^(k-1)`,
so `ar^(k-1)=162`.

The sum of the first `k` terms is
`S_k=a(1-r^k)/(1-r)=(a-ar^k)/(1-r)=(a-(ar^(k-1))r)/(1-r)=1562`

Substituting,we get:

`(a-162(3/4))/(1-(3/4))=1562`

Algebra gives us `a=512`

Arithmetical

Work backwards from the `k` th term.

`1/r = 4/3`

The `k-1` th term is `162*4/3=216`.

The sum `216+162 < 1562`, so keep working backwards:

The previous term is `216 * 4/3=288` and the sum is still too small.

Continue until we get: The terms we need are:

`512+384+288+216+162`