Question

What is the 15th term of the following sequence? -0.25, 0.5, 1.25, 2, 2.75...

Answer 1

The 15th term is 10.25

Explanation:

Sequences

The given sequence:

-0.25, 0.5, 1.25, 2, 2.75...

can be categorized as an arithmetic sequence. To better know, we try to find a common difference between successive terms:

0.5 - (-0.25) = 0.75

1.25 - 0.5 = 0.75

2 - 1.25 = 0.75

Once we are certain it's an arithmetic sequence, we find the general term by using the formula:

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

Where n is the number of the term, a1 is the first term, and r is the common difference. We have already found that:

r=0.75

a1=-0.25

The 15th term (n=15) is:

`a_(15)=-0.25+(15-1)*0.75`

`a_(15)=-0.25+14*0.75`

`a_(15)=-0.25+10.5=10.25`

The 15th term is 10.25