# Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1= -34, d=-10?

Jul 17, 2015

The explicit formula for the sequence is $\textcolor{red}{{a}_{n} = - 10 n - 24}$, and the first five terms are $\textcolor{red}{- 34 , - 44 , - 54 , - 64 , - 74}$.

#### Explanation:

We know that the common difference $d = - 10$.

The general formula for an arithmetic sequence is

${a}_{n} = {a}_{1} + \left(n - 1\right) d$.

So, for your sequence, the general formula is

${a}_{n} = - 34 + \left(n - 1\right) \left(- 10\right) = - 34 - 10 n + 10$

${a}_{n} = - 10 n - 24$

${a}_{1} = - 34$

a_2 = -10×2-24 = -20-24 = -44

a_3 = -10×3-24 = -30-24 = -54

a_4 = -10×4-24 = -40-24 = -64

a_5 = -10×5-24 = -50-24 = -74

The first five terms are $- 34 , - 44 , - 54 , - 64 , - 74$.