Question

Identify the 25th term of the arithmetic sequence 2,1 (3 / 5), 1 ( 1 / 5) ... (2 points)

Answer 1

Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial value, d=common difference, n=term number.

The common difference is the constant difference found by subtracting the previous term from any term.  In this case:

d=2-1 3/5=1 3/5-1 1/5=-2/5=-0.4  and we can easily see that the first term is 2 so

a(n)=2-0.4(n-1)  which can be simplified...

a(n)=2-0.4n+0.4

a(n)=2.4-0.4n, so the 25th term is:

a(25)=2.4-0.4(25)

a(25)= -7.6  or if you prefer...

a(25)= -7 3/5