Math

QuestionFind the 13th term of the sequence given by an=84+(n1)(6)a_{n}=84+(n-1)(-6). A. 156 B. 12 C. 2 D. 162

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the arithmetic sequence is given by an=84+(n1)(6)a_{n}=84+(n-1)(-6). We need to find the13th term in the sequence, i.e., a13a_{13}

STEP 2

We can find the13th term by substituting n=13n =13 into the explicit formula.
a13=84+(131)(6)a_{13}=84+(13-1)(-6)

STEP 3

First, calculate the value inside the parentheses.
a13=84+(12)(6)a_{13}=84+(12)(-6)

STEP 4

Next, perform the multiplication.
a13=84+(72)a_{13}=84+(-72)

STEP 5

Finally, perform the addition to find the13th term.
a13=8472a_{13}=84-72

STEP 6

Calculate the value of a13a_{13}.
a13=12a_{13}=12So, the13th term in the arithmetic sequence is12.

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