Given an arithmetic sequence with a1=88 and a9=12 find the common difference d.

Question

What is the common difference? 

Answer 1

In an arithmetic sequence, the nth term, a_n, is given by the formula:

 

a_n = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference.  

 

So, a₉ = a₁ + 8d

 

Substituting in the given data, 12 = 88 + 8d

                                                     -76 = 8d

                                                       d = -76/8 = -19/2

Answer 2

Between term 1 and term 9, you've dropped by 76. This is a drop of 76 in 8 drops, since you're starting at a1. (That is, a1 to a2 is first drop, a2 to a3 is the second drop, etc.)

 

d = total drop/number of drops.

 

You can check your answer by writing out all 8 terms a1 to a9 and verifying they're d units apart.