Evaluate the series. $\sum _ { i = 1 } ^ { 4 } ( 4 i + 3 ) ( 3 i - 4 )$
A) $15$
B) $242$
C) $873$
D) $495$
E) $2100$

Question

Quizplus · Accepted Answer

The series can be evaluated by calculating each term individually and then summing them up. The general term of the series is $(4i + 3)(3i - 4)$. We calculate this for $i = 1, 2, 3, 4$ and sum the results.For $i = 1$, the term is $(4*1 + 3)(3*1 - 4) = (7)(-1) = -7$.For $i = 2$, the term is $(4*2 + 3)(3*2 - 4) = (11)(2) = 22$.For $i = 3$, the term is $(4*3 + 3)(3*3 - 4) = (15)(5) = 75$.For $i = 4$, the term is $(4*4 + 3)(3*4 - 4) = (19)(8) = 152$.Summing these results gives: $-7 + 22 + 75 + 152 = 242$.

Evaluate the Series ∑i=14(4i+3)(3i−4)\sum _ { i = 1 } ^ { 4 } ( 4 i + 3 ) ( 3 i - 4 )∑i=14​(4i+3)(3i−4)

Evaluate the Series $\sum _ { i = 1 } ^ { 4 } ( 4 i + 3 ) ( 3 i - 4 )$