Question

An arithmetic sequence is as follows: 2, 24, 46... find the 4th, 5th, and 6th terms

Answer 1

`a_n=a_1+(n-1)d`

where: an - nth term, a1 - first term, and d- common difference

For the arithmetic sequence, 2, 24, 46

a1 = 2

d = 24-2 = 22

or d = 46-24 = 22 ( also 22)

for the 4th term, n =4

substituting the values in the formula

for the 4th term, n =4; a4 = 2 + ( 4 - 1 ) (22) = 2 + (3)(22) = 2 + 66 = 68

for the 5th term, n =5; a5 = 2 + ( 5 - 1 ) (22) = 2 + (4)(22) = 2 + 88 = 90

for the 6th term, n =6; a6 = 2 + ( 6 - 1 ) (22) = 2 + (5)(22) = 2 + 110 = 112

To check, 90 - 68 = 112 - 90 = 22

Answer 4th = 68, 5th = 90 and 6th = 112