Question

the first three terms of a sequence are given. write your answer as a decimal or whole number. round to the nearest thousandth (if necessary). 205, 201, 197, ... find the 48th term. answer attempt 1 out of 2

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence with first term \( a_1 = 205 \) and common difference \( d = 201 - 205 = -4 \).

Step2: Use the arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \).

Step3: Substitute values for the 48th term

For \( n = 48 \), \( a_1 = 205 \), \( d = -4 \):
\( a_{48} = 205 + (48 - 1)(-4) \)
\( = 205 + 47\times(-4) \)
\( = 205 - 188 \)
\( = 17 \)

Answer:

17