Question

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence? 14/13 25/7 4

Answer 1

`a_1=-3 \\ a_(15)=53 \\ \\ d= (53-(-3))/(15-1)= (56)/(14)=4`

The answer is d=4

Answer 2

The common difference of the arithmetic sequence is:

4

Explanation:

We kn ow that if the first term of an arithmetic sequence is a and d is the common difference of the sequence then the nth term of the sequence is given by the formula:

`a_n=a+(n-1)d`

Here we are given:

`a=-3`

and

`a_15=53\\\\i.e.\\\\a+(15-1)d=53\\\\i.e.\\\\a+14d=53`

Now using the value of a we have:

`-3+14d=53\\\\i.e.\\\\14d=56\\\\i.e.\\\\d=4`