What is the fifth term of the arithmetic sequence $2,$ _, $8$ , _, _, ...?

5

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11

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13

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14

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15

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Solution

The correct option is D $14$
We know that $a_{2} = a_{1} + d$
$\Rightarrow a_{3} = a_{2} + d$
So, $a_{1} = 2, a_{3} = 8$
Substitute the values, we get
$a_{2} = 2 + d$
$\Rightarrow 8 = 2 + d + d$
$\Rightarrow 6 = 2 d$
$\Rightarrow d = 3$
So, the arithmetic sequence is $2, 5, 8, 11, 14$ .
Therefore, the fifth term is $14$ .

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