Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-$$\sum _ { i = 1 } ^ { 4 } \left( \frac { 3 } { 4 } \right) i + 1$$
A) $\frac { 1575 } { 1024 }$
B) $\frac { 525 } { 256 }$
C) $\frac { 1579 } { 1024 }$
D) $\frac { 7029 } { 1024 }$

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula:$$S_n = \frac{a(1 - r^n)}{1 - r}$$where a is the first term, r is the common ratio, and n is the number of terms.In this case, a = 3/4, r = 3/4, and n = 4. So, the sum of the first 4 terms is:$$S_4 = \frac{\frac{3}{4}(1 - (\frac{3}{4})^4)}{1 - \frac{3}{4}} = \frac{\frac{3}{4}(1 - \frac{81}{256})}{\frac{1}{4}} = \frac{\frac{3}{4}(\frac{175}{256})}{4} = \frac{1575}{1024}$$Therefore, the correct answer is A.

Find the Indicated Sum ∑i=14(34)i+1\sum _ { i = 1 } ^ { 4 } \left( \frac { 3 } { 4 } \right) i + 1i=1∑4​(43​)i+1

Find the Indicated Sum $\sum _ { i = 1 } ^ { 4 } \left( \frac { 3 } { 4 } \right) i + 1$