Question

What is the next term in this sequence: 76, 80, 88, 95, 100, 101


I’m stuck

Answer 1

105

Explanation:

Answer 2

112

Explanation:

Given the sequence 76, 80, 88, 95, 100, 101... Before we can get the next term of the sequence, we must first understand the pattern. We are not going to be considering all the terms of the sequence. In the sequence, only the following values forms a pattern as shown;

76, 88, 100... This are the first, third and fifth term of the sequence. The next term will be the 7th term of the sequence and the 4th term of the extracted sequence which is what we are looking for.

Note that the extracted forms an arithmetic sequence with 76 as its first term and 12 as its common diffidence (i.e 88-76 = 100-88).

Using the nth term of an AP to find the next term of the sequence we have;

`Tn = a + (n-1)d`

a is the first term = 76

d is the common difference = 12

n is the number of terms = 4 (since we are looking for the 4th term of the extracted sequence)

`T4 = 76+(4-1)*12\\T4 = 76 + (3*12)\\T4 = 76 + 36\\T4 = 112`

The next term in the sequence is 112