Question

What is the common difference for the arithmetic sequence: 8.6, 6.2, 3.8, 1.4, −1, −3.4, …

Answer 1

So the common difference is -2.4

Explanation:

In an arithmetic sequence the common difference is the difference between any two consecutive terms

also formula for common difference is d= a(n) - a(n-1)

which means that if we have an arithmetic sequence i.e. a1,a2,a3 and a4

then their common difference will be

common difference = a₂-a₁= a₃-a₂ = a₄ -a₃

Now for the given sequence

Common difference = 6.2 - 8.6

= - 2.4

Check:

8.6 - 2.4 = 6.2

6.2 - 2.4 = 3.8

3.8 - 2.4 = 1.4

.

.

So the common difference is -2.4

Answer 2

Explanation:

If you start with t1 = 8.6

and t2 = 6.4

Then tn - tn-1 = 6.4 - 8.6 = -2.4

In other words if you start at tn-1 and go to the next term tn you have to subtract 2.4 from the term to get to the next term.

t1 = 8.6

t2 = 6.2

t2 = 8.6 - 2.4 = 6.2

The difference is -2.4

In general tn+1 = tn - 2.4