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

Feb 27, 2018

$206$ is the $35$th term.

#### Explanation:

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

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

${a}_{n} = {a}_{1} + \left(n - 1\right) d$

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

${a}_{n} = 2 + 6 \left(n - 1\right)$

${a}_{n} = 2 + 6 n - 6$

${a}_{n} = 6 n - 4$

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

${a}_{35} = 6 \cdot 35 - 4$

${a}_{35} = 210 - 4$

${a}_{35} = 206$