Question

find the sum of the first 8 terms of the gp 1,3,9,27,81

Answer 1

Looking at the series of numbers, you can see that any number is 3 times the number right before it. So with each additional term, you have multiplied a number by 3 one more time. This means that terms in the series can be rewritten as 3^0, 3^1, 3^2, 3^3, etc. So to find a relationship for the nth term will mean finding an exponent where the base is three. You'll notice that the first term has an exponent of 0, the second term has an exponent of 1, the third term has an exponent of 2, so the exponent is always one less than the number for the term. In other words (n-1) is the exponent for the nth term. So the required expression becomes 3^(n-1).