Geometric Sequence - Sum to Infinity

**Tesphen** · May 20th 2009, 01:52 PM

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.

**e^(i*pi)** · May 20th 2009, 01:59 PM

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: $U_n = ar^{n-1}$

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 $U_2 = ar = 18$ (eq1)
$U_4 = ar^3 = 2$ (eq2)

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

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: $S_{\infty} = \frac{a}{1-r}$

I get an answer of 81

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