Question

Use the formula to evaluate the series 2 - 10 + 50 -250 + ... a6 sn = a1(1-r^n) / 1-r

Answer 1

The given is a geometric sequence where the consecutive terms have a common ratio of -5. The first term is given to be 2 and the number of terms is 6. If we are to substitute the known variables to the equation,

Sn = (2)(1 – (-5)^6) / (1 - -5)

The value of Sn from the equation is -5208. Thus, the sum of the first six terms of the geometric sequence is -5208.