Find the indicated partial sum for the given sequence with the given first term and general term
-$\mathrm{s}_{4}, \mathrm{a}_{1}=4, \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{\mathrm{n}}-1+7$
A) 90
B) 58
C) 33
D) 54

Question

Quizplus · Accepted Answer

The given sequence starts with $a_1 = 4$ and each term is obtained by adding 7 to the previous term ($a_n = a_{n-1} + 7$). This is an arithmetic sequence with a common difference of 7. The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $d$ is the common difference. To find the 4th term ($a_4$), we use $a_4 = 4 + (4 - 1) \times 7 = 4 + 3 \times 7 = 4 + 21 = 25$. The partial sum of the first 4 terms ($s_4$) can be found using the formula $s_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms. Thus, $s_4 = \frac{4}{2}(4 + 25) = 2 \times 29 = 58$.

Find the Indicated Partial Sum for the Given Sequence with the Given