The first three term of a sequence are given: 2,8,14. Find the 35th term?

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Answer 1 · 2018-02-27T14:02:44

$206$ $206$ is the $35$ $35$ th term.

This is an arithmetic sequence, where $d$ $d$ is the common difference between two consecutive items.

Generally, the $n$ $n$ th term, $a_{n}$ $a_n$ , of an arithmetic series is given by:

$a_{n} = a_{1} + (n - 1) d$ $a_n=a_1+(n-1)d$

Here, $a_{1} = 2$ $a_1=2$ , the first term, and $d = 6$ $d=6$ . We can input these two values into the general equation:

$a_{n} = 2 + 6 (n - 1)$ $a_n=2+6(n-1)$

$a_{n} = 2 + 6 n - 6$ $a_n=2+6n-6$

$a_{n} = 6 n - 4$ $a_n=6n-4$

This is the formula for this sequence. We can use the general equation, but this works too, and it is simpler. Inputting $n = 35$ $n=35$ , we get:

$a_{35} = 6 \cdot 35 - 4$ $a_35=6*35-4$

$a_{35} = 210 - 4$ $a_35=210-4$

$a_{35} = 206$ $a_35=206$