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Chapter 8: Problem 34

Find the indicated sum. Use the formula for the sum of the first \(n\) terms of a geometric sequence. $$\sum_{i=1}^{7} 4(-3)^{i}$$

Short Answer

Expert verified
By applying the formula for the sum of a geometric sequence, we find that the sum of the series is \(2720\).

Step by step solution

01

Identify the Parameters

The first term (a_1) is \(4 * (-3)^1 = -12\) and the common ratio (r) is -3. The number of terms (n) is 7.
02

Apply the Formula

Plug these values into the general formula for the sum of a geometric sequence: \(S_n = a_1 * (1 - r^n) / (1 - r)\)
03

Calculate the Sum

After substituting the values into the equation, we get \(S_7 = -12 * (1 - (-3)^7) / (1 - -3)\). Calculate this expression to find the sum.

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