Math

QuestionFind the 10th term in the arithmetic sequence 11,19,27,35,43,11, 19, 27, 35, 43, \ldots. Options: 91,75,100,8391, 75, 100, 83.

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence. The formula for the nth term of an arithmetic sequence is an=a1+(n1)da_{n}=a_{1}+(n-1) d
3. The first term a1a_{1} is114. The common difference dd can be calculated as the difference between the second term and the first term

STEP 2

First, we need to find the common difference dd 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 term and the second term to calculate the common difference.
d=1911d =19 -11

STEP 4

Calculate the common difference.
d=1911=8d =19 -11 =8

STEP 5

Now that we have the common difference, we can find the10th term a10a_{10} of the arithmetic sequence using the formula an=a1+(n1)da_{n}=a_{1}+(n-1) d.

STEP 6

Plug in the values for the first term, the common difference, and n =10 into the formula.
a10=11+(101)×8a_{10} =11 + (10 -1) \times8

STEP 7

Calculate the10th term.
a10=11+9×=11+72=83a_{10} =11 +9 \times =11 +72 =83So, the10th term of the given arithmetic sequence is83.

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