Question

functions and lines
finding a specified term of an arithmetic sequence given the first terms
find the 78^th term of the following arithmetic sequence.
3, 8, 13, 18, ...

Explanation:

Step1: Identify a₁ and d

For the arithmetic sequence \( 3, 8, 13, 18, \dots \), the first term \( a_1 = 3 \). The common difference \( d \) is \( 8 - 3 = 5 \).

Step2: Use arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \). We need to find the 78th term, so \( n = 78 \). Substitute \( a_1 = 3 \), \( d = 5 \), and \( n = 78 \) into the formula:
\( a_{78} = 3 + (78 - 1) \times 5 \)
First, calculate \( 78 - 1 = 77 \). Then, \( 77 \times 5 = 385 \). Finally, \( 3 + 385 = 388 \).

Answer:

388