Thread: Geometric Sequence - Sum to Infinity

The second term of a geometric progression is 18 and the fourth term is 2. The common ratio is positive. Find the sum to infinity of this progression.

If anyone could help me with this question it'd be greatly appreciated.

I tried using the a / 1 - r formula and it din't give the right answer.

Originally Posted by Tesphen

The second term of a geometric progression is 18 and the fourth term is 2. The common ratio is positive. Find the sum to infinity of this progression.

If anyone could help me with this question it'd be greatly appreciated.

I tried using the a / 1 - r formula and it din't give the right answer.

In general: $\displaystyle U_n = ar^{n-1}$

where Un is the nth term, a is the first term, r is the common ratio and n is the number of terms.

We know $\displaystyle U_2 = ar = 18$ (eq1)
$\displaystyle U_4 = ar^3 = 2$ (eq2)

eq2/eq1 = $\displaystyle \frac{ar^3}{ar} = \frac{2}{18} = \frac{1}{9}$

Solve that for r (remember r>0) and then find a using either eq1 or eq2.

Once you have a and r put them into the general formula: $\displaystyle S_{\infty} = \frac{a}{1-r}$

I get an answer of 81