# Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1= -38, d=-100?

Jun 18, 2015

${a}_{1} = - 38 , {a}_{2} = - 138 , {a}_{3} = - 238 , {a}_{4} = - 338 , {a}_{5} = - 438$
${a}_{n} = 62 - 100 n$

#### Explanation:

To calculate the consecutive terms just add $d$ to ${a}_{1}$, so you get:
${a}_{2} = {a}_{1} + r = - 38 + \left(- 100\right) = - 138$
${a}_{3} = a - 2 - 100 = - 138 - 100 = - 238$
and so on

To find the formula just substitute ${a}_{1}$ and $r$ in
${a}_{n} = {a}_{1} + \left(n - 1\right) r$

${a}_{n} = - 38 - 100 \left(n - 1\right) = - 38 - 100 n + 100 = 62 - 100 n$