Question

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

A) 8/9
B) 1.8
C) 2

Any help will be greatly appreciated!

Answer 1

Basically use the number line ide, -5 to 13 is 18 apart. Ten apart, don't count the first one, so 9. 18/9= 2 apart C is your answer

Answer 2

The common difference be 2.

Option(C) is corrct .

Explanation:

As given

The first term of an arithmetic sequence is -5, and the tenth term is 13.

As the the terms in arithmetic sequence is in the form.

`a_(n) = a_(1) + (n - 1)d`

`a_(n) = n^(th)\ term`

`a_(1) = 1^(th)\ term`

d is the common difference .

As
`a_(1) = - 5`

n = 10

`a_(10) = 13`

Put in the above

`a_(10) = a_(1) + (10 - 1)d`

`13 = -5 + (10 - 1)d`

`13 + 5 = 9d`

`18= 9d`

`d = (18)/(9)`

d = 2

Therefore the common difference be 2.

Option(C) is corrct .