Question

Find the 100th term of the following arithmetic sequence
5.5, 6, 6.5, 7, ...

Answer 1

55.

Explanation:

The explicit formula for the nth term is a1 + d(n - 1).

Here d = 6 - 5.5 = 0.5 and a1 = 5.5.

So the 100th term = 5.5 + 0.5(100-1)

= 55.

Answer 2

55

Explanation:

The n-th term of an arithmetic sequence is given by the formula ...

an = a1 + d(n -1)

where a1 is the first term (5.5) and d is the common difference (0.5).

So, the n-th term is ...

an = 5.5 +0.5(n -1) = 5.0 +0.5n

For n = 100, the term is ...

a100 = 5.0 +0.5(100) = 55

The 100th term of the sequence is 55.