# What is the 30th term of the following sequence 2, 8, 14, 20?

Aug 7, 2016

${T}_{30} = 176$

#### Explanation:

By finding the difference (subtracting) the consecutive terms, we fins that the terms differ by 6. SO the next term would be 20+6 .... and so on. This is an A.P.

The general term for an AP is given by
${T}_{n} = a + \left(n - 1\right) d$,
$a$ = first term = 2
$n$ = number of terms, or the position of a particular term,
$d$ = common difference = 6
${T}_{n}$ is the value of a term in a particular position.

In this case .. ${T}_{5} = 26$

${T}_{30} = 2 + 29 \left(6\right)$

${T}_{30} = 176$