Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1 2 , 1 4 , 1 6 , 1 8 , 1 10 , ...

Answer 1

Answer:

1•2n

Step-by-step explanation:

Given the sequence if numbers

1 2 , 1 4 , 1 6 , 1 8 , 1 10 , ...

You will see that 1 is common to all the numbers, the other part of the sequence are in arithmetic progression and they are

2,4,6,8,10...

The nth term of an AP is expressed as

Tn = a+(n-1)d

a is the first term

n is the number of terms

d is the common difference

a = 2

d = 4-2 = 6-4 = 8-6 = 2

Substitute into the formula

Tn = 2+(n-1)2

Tn = 2+2n-2

Tn = 2-2+2n

Tn = 2n

Hence the nth term of the sequence is 1•2n