# Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

Jul 17, 2015

The explicit formula for the sequence is $\textcolor{red}{{a}_{n} = 4 n + 31}$, and the first five terms are $\textcolor{red}{35 , 39 , 43 , 47 , 51}$.

#### Explanation:

We know that the common difference $d = 4$.

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

${a}_{n} = 35 + 4 \left(n - 1\right) = 35 + 4 n - 4$

${a}_{n} = 4 n + 31$

${a}_{1} = 35$

a_2 = 4×2+31 = 8+31 = 39

a_3 = 4×3+31 = 12+31 = 43

a_4 = 4×4+31 = 16+31= 47

a_5= 4×5+31 = 20+31 = 51

The first five terms are $35 , 39 , 43 , 47 , 51$.