Questions: Consider the sequence (an) whose terms are (3,8,13,18,23,28,33 ...). What is the value of (sumn=4^7 an) ? a.) 126 b.) 84 c.) 69

Transcript text: Consider the sequence $a_{n}$ whose terms are $(3,8,13,18,23,28,33 \ldots)$. What is the value of $\sum_{n=4}^{7} a_{n}$ ? a.) 126 b.) 84 c.) 69

Solution

Solution Steps

Step 1: Identify the Sequence

The given sequence is $a_n = 3, 8, 13, 18, 23, 28, 33, \ldots$. This is an arithmetic sequence where the first term $a_1 = 3$ and the common difference $d = 5$.

Step 2: Find the General Formula

The general formula for the $n$-th term of an arithmetic sequence is given by:

\[ a_n = a_1 + (n-1) \cdot d \]

Substituting the known values:

\[ a_n = 3 + (n-1) \cdot 5 = 5n - 2 \]

Step 3: Calculate the Required Terms

We need to find the sum $\sum_{n=4}^{7} a_n$. First, calculate each term: