Question

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?

Answer 1

T15=a+(n-1)d where: "T15" is the 15th term, "a" is the 1st term, "n" is the number of terms and "d" is the common diff.Thus; 53=-3+(15-1)d 53=-3+14d 53+3=14d 56=14d d=56/14 d=4

Answer 2

the common difference = 4

Explanation:

First term of an arithmatic sequence is -3

15th term is 53

We need to find the common difference 'd'

Formula for nth term of the sequence is

`a_n= a_1+(n-1)d`

where a_1 is the first term and d is the common difference

a1= -3

Lets plug in 15 for n

`a_n= a_1+(n-1)d`

`a_(15)= -3+(15-1)d`, solve for d

`53= -3+(15-1)d`

Add 3 on both sides

`56=(14)d`

Divide both sides by 14

d=4

So, the common difference = 4