Question

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

Answer 1

Answer:

The second term is 4.5

Step-by-step 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  

Answer 2

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