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* 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*1+c \\ 31=-7+c \\ c=38 \end{gathered}`

now the explicit formula is

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