Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 42 } ( 2 i + 3 )$$
A) 1932
B) 1890
C) 2100
D) 2247

Question

Quizplus · Accepted Answer

The given sum can be simplified to find the sum of an arithmetic sequence. The formula for the sum of the first n terms of an arithmetic sequence is $S_n = \frac{n}{2} [2a + (n - 1)d]$, where $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. In this case, the first term when $i = 1$ is $2(1) + 3 = 5$, and the common difference $d$ is 2 (since each term increases by $2i$, and for each consecutive term, $i$ increases by 1, thus adding 2 to the sequence each time). Plugging into the formula: $S_{42} = \frac{42}{2} [2(5) + (42 - 1)2] = 21[10 + 82] = 21 \times 92 = 1932$.

Use the Formula for the Sum of the First N ∑i=142(2i+3)\sum _ { i = 1 } ^ { 42 } ( 2 i + 3 )i=1∑42​(2i+3)

Use the Formula for the Sum of the First N $\sum _ { i = 1 } ^ { 42 } ( 2 i + 3 )$