Question

Find the common difference of the arithmetic sequence, the next three terms, the equation, and the term given for 8, 10, 12, 14

Answer 1

see explanation

Explanation:

In an arithmetic sequence the common difference d is

d = a₂ - a₁ = 10 - 8 = 2

To obtain the next term in the sequence add d to the previous term, that is

a₅ = 14 + 2 = 16

a₆ = 16 + 2 = 18

a₇ = 18 + 2 = 20

The next 3 terms in the sequence are 16, 18, 20

The n th term equation for an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = 2, thus

`a_(n)` = 8 + 2(n - 1) = 8 + 2n - 2 = 2n + 6