Question

Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 39, d=-5?

Answer 1

The first five terms are: `39, 34,29,24,19`
and
`color(blue)(a_n=34-5n` for `n=1,2,3....`

Explanation:

The first number of the sequence is
`a_1 =39`
and the common difference is
`d=-5`

All subsequent terms for the arithmetic sequence can be found by simply adding the common difference to the preceding term.
`a_2 = a_1 +d = 39 +(-5)`
`a_2 = 34`
`a_3 = a_2 +d = 34 +(-5) = 29`
`a_4 = a_3 +d = 29+(-5) =24`
`a_5 =a_4 +d= 24 +(-5)=19`

The explicit formula is
`a_n = a_1+(n-1)d`
`a_n=39+(n-1)* (-5)`
`a_n=39-5n-5`
`color(blue)(a_n=34-5n` (for `n=1,2,3....`)