Solving for terms in an arthmetic sequence.

Question

The terms 5+X, 8, and 1+2x are consecutave erms in an arithmetic sequence. Determine the value of x and state the three terms
how do you go about solving this?

Answer 1

The difference between 8 and 1 + 2x is the same as the difference between 5 + x and 8.

Difference between 8 and 1 + 2x is (1 + 2x) - 8 = 2x - 7
Difference between 5 + x and 8 is 8 - (5 + x) = 3 - x

Thus, we have:

2x - 7 = 3 - x
2x + x = 3 + 7
3x = 10
x = 10 / 3

5 + x
= 5 + 10/3
= 15/3 + 10/3
= 25/3

1 + 2x
= 1 + 2(10/3)
= 3/3 + 20/3
= 23/3

Hence, the terms are 25/3, 8, 23/3

Note that 8 = 24 / 3

Comments

Thanks so much. Perfect.