In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.
A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding term multiplied by r. So, we can assign values to a and ar^3 given we have been provided with the first and fourth terms. Now to find r. 256/2048 is the same as ar^3/a. The a's cancel out, which tells us r^3 is 1/8 and so r is 1/2. You need to know a formula to answer the next part. The sum for n terms in a geometric series is S = a(1-r^n)/(1-r). We know values for a, r and S, and we wish to determine a value for n. Solving this equation leads to n = 10.
SW
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