Question

Write the sum using summation notation, assuming the suggested pattern continues. 4 - 12 + 36 - 108 + ...

Answer 1

9514 1404 393

Answer:

`\displaystyle S_n=\sum_(k=1)^n{4(-3)^(k-1)}`

Explanation:

The first term of this geometric series is 4. The common ratio is -12/4 = -3, so the general term is ...

an = 4·(-3)^(n-1)

The sum is the sum of terms of this form.

`\displaystyle S_n=\sum_(k=1)^n{4(-3)^(k-1)}`