Math

QuestionFind a formula for ana_{n}, the nthn^{\text{th}} term of the sequence 36,44,52,36, 44, 52, \ldots.

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning that the difference between consecutive terms is constant. . The first term of the sequence is36.
3. The second term of the sequence is44.
4. The third term of the sequence is52.

STEP 2

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the first term from the second term.
d=a2a1d = a_{2} - a_{1}

STEP 3

Now, plug in the given values for the first and second terms to calculate the common difference.
d=4436d =44 -36

STEP 4

Calculate the common difference.
d=4436=8d =44 -36 =8

STEP 5

Now that we have the common difference, we can write the explicit formula for the nth term of an arithmetic sequence. The formula isan=a1+(n1)da_{n} = a_{1} + (n -1) \cdot d

STEP 6

Plug in the values for the first term and the common difference into the formula.
an=36+(n1)8a_{n} =36 + (n -1) \cdot8

STEP 7

implify the formula.
an=36+na_{n} =36 +n -

STEP 8

Combine like terms.
an=28+8na_{n} =28 +8nSo, the explicit formula for the nth term of the sequence is an=28+8na_{n} =28 +8n.

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