Question

The first 4 terms of a geometric series are:14 + 14/3 + 14/9 + 14/27a)Find r, the common ratio of the series.b) Form and simplify an expression for un, the nth term of the series.C)Find the 7th term of the series, giving the answer as a fraction.[2 marks]d) Form and simplify an expression for Sm, the sum to the nth term of the series.e) Find the sum to the 6th term of the series, giving the answer as a fraction.f)Find So, the sum to infinity of the series.

Answer 1

The given series is:

$14+\frac{14}{3}+\frac{14}{9}+\frac{14}{27}+\ldots$

Recall that the common ratio is the ratio between each pair of consecutive terms in a geometric series.

Hence, to calculate the common ratio, evaluate the ratio of any consecutive terms:

$\frac{\frac{14}{3}}{14}=\frac{14}{3\times14}=\frac{1}{3}$

Hence, the common ratio is 1/3.