Question

Write the formula for the n th term of the arithmetic sequence 4,6,8,10. Use the formula to find a8

Answer 1

Explanation:

An arithmetic sequence is a sequence in which each term differs from the term following it by a common difference. This common difference is constant between two consecutive terms. The formula for the nth term of an arithmetic sequence is expressed as

Tn = a +(n - 1)d

Where

a is the first term of the sequence

d is the common difference.

Tn is the nth term

n is the number of terms in the sequence

Looking at the information given,

a = 4

d = 6 - 4 = 8 - 6 = 2

To find a8, it will be the eighth term. Therefore

a8 = 4 + (8 - 1)2

a8 = 4 + 7×2

a8 = 4 + 14 = 18

Answer 2

• an = 4 + 2(n-1)
• a8 = 18

Explanation:

The n-th term is given by ...

an = a1 + d(n -1)

for common difference d and first term a1.

You have a sequence with a first term 4 and a common difference of 6-4=2, so the formula is ...

an = 4 + 2(n -1)

__

Using n=8, we find ...

a8 = 4 + 2(8-1)

a8 = 18