Problem 34
Question
Find the indicated sum. Use the formula for the sum of the first \(n\) terms of a geometric sequence. $$\sum_{i=1}^{7} 4(-3)^{i}$$
Step-by-Step Solution
Verified Answer
By applying the formula for the sum of a geometric sequence, we find that the sum of the series is \(2720\).
1Step 1: 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.
2Step 2: Apply the Formula
Plug these values into the general formula for the sum of a geometric sequence: \(S_n = a_1 * (1 - r^n) / (1 - r)\)
3Step 3: 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.
Other exercises in this chapter
Problem 34
Some statements are false for the first few positive integers, but true for some positive integer on. In these instances, you can prove \(S_{n}\) for \(n \geq k
View solution Problem 34
Use the formula for \(_{n} P_{r}\) to solve Exercises \(33-40\) A corporation has ten members on its board of directors. In how many different ways can it elect
View solution Problem 34
Find each indicated sum. $$\sum_{k=1}^{4}(k-3)(k+2)$$
View solution Problem 35
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(x^{2}+1\right)^{16} $$
View solution