Question

An arithmetic sequence is given below.31, 24, 17, 10, ... Write an explicit formula for the

Answer 1

let's detect the sequence, between the numbers there is a difference of 7

then, the next number is always 7 units less

the general formula is

$a_n=(d\times n)+c$

where d is the common diference , n the position of the number,an the result and c a constant

we know d=-7 , now we need c

we can do it replacing an=31 and n=1

because 31 is the result of the fiste number

$\begin{gathered} 31=-7\times1+c \\ 31=-7+c \\ c=38 \end{gathered}$

now the explicit formula is

$a_n=-7n+38_{}$