Question

Find the 13th term in the following arithmetic sequence: 2, 10, 18, 26...

Answer 1

Given:

`2,8,10,18,26\ldots`

The above series is an arithemetic series.

The first term of the series is: a=2

The second term of the series is: b=10

The common difference of the series is,

`\begin{gathered} d=b-a \\ =10-2 \\ =8 \end{gathered}`

The expression to calculate the n th term of the series is,

`a_n=a+(n-1)d`

Substitute n=13 in the above expression to calculate the 13 th term.

`\begin{gathered} a_(13)=2+(13-1)*8 \\ =2+12*8 \\ =2+96 \\ =98 \end{gathered}`

Thus, the 13th term of the sequence is 98.