Question

Find the 11th term of the arithmetic sequence. a3 = 20.5 and a8 = 13, a11 = ______. ...?

Answer 1

In order to solve for a nth term in an arithmetic sequence, we use the formula written as:

an = a1 + (n-1)d

where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.

First, we need to calculate for d from the given values above.  
a3 = 20.5 and a8 = 13


an = a1 + (n-1)d
20.5 = a1 + (3-1)d

an = a1 + (n-1)d
13 = a1 + (8-1)d

a1 = 23.5
d = -1.5

The 11th term is calculated as follows:

a11 = a1 + (n-1)d
a11= 23.5 + (11-1)(-1.5)
a11 = 8.5