Question

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).

361, 354, 347, ...

find the 47th term.

Explanation:

Step1: Identify sequence type, find $d$

Calculate common difference: $d = 354 - 361 = -7$

Step2: Recall arithmetic sequence formula

The $n$-th term formula: $a_n = a_1 + (n-1)d$

Step3: Substitute values for $n=47$

$a_{47} = 361 + (47-1)(-7)$

Step4: Compute the result

First calculate $(47-1)(-7) = 46\times(-7) = -322$, then $361 - 322 = 39$

Answer:

39