Question

What is the common difference, d, of the sequence?

9, −8, −25, −42, −59, ...


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Answer 1

we substract going backwards
-59-(-42)=-17
-42-(-25)=-17
-25-(8-)=-17
-8-9=-17
our common difference is equal to -17

Answer 2

This question is determined  by using the concept of sequence. Therefore, the common difference is -17.    

Given:

Sequence is 9, −8, −25, −42, −59, ...

We need to determined the  common difference, d, of the sequence.

Here,  $a_1 = 9, a_2=-8,a_3 = -25, a_4= -42, a_5= -59$

Now, calculate the common difference d by using the formula,

$d = a_{n+1} - a_n$

Now, put the value n = 1  in above formula.

We get,

$d_1= a_{1+1} - a_1\\d_1=a_2-a_1\\d_1 = -8-9\\d_1 = -17$                        $d_2= a_{2+1} - a_2\\d_2=a_3-a_2\\d_2 = -25-(-8)\\d_2 = -17$

Here,  $d_1 = d_2$, therefore, the common difference is -17.    

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