# 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?

Aug 31, 2015

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

#### 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.
${a}_{2} = {a}_{1} + d = 39 + \left(- 5\right)$
${a}_{2} = 34$
${a}_{3} = {a}_{2} + d = 34 + \left(- 5\right) = 29$
${a}_{4} = {a}_{3} + d = 29 + \left(- 5\right) = 24$
${a}_{5} = {a}_{4} + d = 24 + \left(- 5\right) = 19$

The explicit formula is
${a}_{n} = {a}_{1} + \left(n - 1\right) d$
${a}_{n} = 39 + \left(n - 1\right) \cdot \left(- 5\right)$
${a}_{n} = 39 - 5 n - 5$
color(blue)(a_n=34-5n (for $n = 1 , 2 , 3. \ldots$)