Find the n th partial sum of the arithmetic sequence. $a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13$
A) 52.65
B) 92.30
C) 105.30
D) 46.15
E) 49.40

Question

Quizplus · Accepted Answer

The nth partial sum of an arithmetic sequence can be found using the formula $S_n = \frac{n}{2} [2a_1 + (n-1)d]$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. First, find the common difference $d$. Since $a_5 = a_1 + 4d$, we have $2.8 = 0.8 + 4d$, leading to $d = 0.5$. Then, use the formula to find the 13th partial sum: $S_{13} = \frac{13}{2} [2(0.8) + (13-1)(0.5)] = \frac{13}{2} [1.6 + 6] = \frac{13}{2} \times 7.6 = 49.4$.

Find the N Th Partial Sum of the Arithmetic Sequence a1=0.8,a5=2.8,…,n=13a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13a1​=0.8,a5​=2.8,…,n=13

Find the N Th Partial Sum of the Arithmetic Sequence $a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13$