Question

In a sequence of 10 terms, the first term is 1, the second term is x, and each term after the second is the sum of the previous two terms. Is 12 the fifth term in the sequence?

Answer 1

NO, 12 is not the fifth term in the sequence

Explanation:

Given the sequence of 10 terms:

First term a1 = 1

second term a2 = x

third term a3 = a2+a1

Since each term after the second is the sum of the previous two terms then;

a3 = x+ 1

a4 = a3 + a2

a4 = x+1+x

a4 = 2x+1

Also

a5 = a4+a3

a5 = 2x+1+x+ 1

a5 = 3x+2

Get x:

The common difference d = a2-a1 = a3-a2

d = x-1 = x+1-x

x-1 = x+1-x

x-x+x = 1+1

x = 2

Get the fifth term:

Recall that a5 = 3x+2

a5 = 3(2)+2

a5 = 6+2

a5 = 8

Hence the fifth term of the sequence is 8 not 12