Question

Find the 2nd term of an arithmetic sequence with t1 = 4 and t5 = 6.

Answer 1

Since it's arithmetic we are adding the same number each time.

4, ____, ____, _____, 6
t1, t2, t3, t4, t5

Subtract 6-4 = 2
Subtract t5 - t1 = 4
divide 2/4 = 1/2 the common difference is 1/2, we are adding 1/2 each time.
4, 4.5, 5, 5.5, 6
The second term is 4.5

Answer 2

The second term is 4.5

Explanation:

An artithmetic sequence is defined as:

An= A1+(n-1) d

Where n is the nth term of the sequence and d is the common difference between terms. We have a1 and d can be found using the fifth term (n=5) like this:

An = A1+(n-1)d

A5 = A1+(5-1)d=A1+4d

D= (A5-A1)/4 = (6-4)/4= 2/4= ½ =0.5

We replace d in the equation for the second term n= 2

A2= a1+(2-1)0.5 = 4+0.5 = 4.5