Write the sum using summation notation, assuming the suggested pattern continues. 5 - 15 + 45 - 135 + ...

As we can see -15 = 5 * (-3); 45 = - 15 * (-3) and so on. This means that a_n = -3 * a_(n-1). The first term in our series is 5 so we obtain

5 - 15 + 45 - 135 + ... = summation from n equals zero to infinity of 5 * (-3)^n.

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