Question

Write a formula for the general term (the nth term) of the arithmetic sequence to find the sixth term of the sequence with the given first term and common difference.

Answer 1

a₆ = 54

Explanation:

The general term of an arithmetic sequence is:
`$ a_1, a_1 + d, a_1 + 2d, a_1 + 3d, \hdots $`

where,
`$ a_1 $` is the first term and

`$ d $` is the common difference.

The
`$ n^(th) $` term of the sequence is given by
`$ a_n = a_1 + (n - 1)d $`.

Therefore,
`$  a_6 = a_1 + (6 - 1)d  = a_1 + 5d $`

`$ \implies a_6 = 14 + 5(8) = 14 + 40 $`

∴ a₆ = 54