Question

find the value of the term in the arithmetic sequence 1,6,11,16...(8th term)

Answer 1

We need to find the 8th term of the following arithmetic sequence:

$1,6,11,16,...$

The formula to find the n-th term an of aₙ arithmetic sequence is:

$a_n=a_1+(n-1)d$

where a₁ is the first term and d is the difference between two consecutive terms.

The first term of this sequence is a₁ = 1, and d is given by:

$\begin{gathered} d=a_2-a_1 \\ \\ d=6-1 \\ \\ d=5 \end{gathered}$

Then, for n = 8, we obtain:

$\begin{gathered} a_8=1+(8-1)5 \\ \\ a_8=1+7(5) \\ \\ a_8=1+35 \\ \\ a_8=36 \end{gathered}$

Answer:

The 8th term is 36.