Question

Identify and extend the pattern to find the next number in this sequence: 22, 35, 48, 61

Answer 1

Find the smallest number which leaves 22,35, 48 and 61 as remainders when divided by 26, 39, 52 and 65 respectively

Answer 2

`A_n=13n`

Next term of sequence: 74

Explanation:

We have been given a sequence of numbers as: 22, 35, 48, 61. We are asked to find the formula that represents the given sequence.

First of all, we will find common difference between two consecutive terms by subtracting any term from its next term as:

`35-22=13`

`48-35=13`

`61-48=13`

This means that common difference is 13.

We know that an arithmetic sequence is in form
`A_n=a+(n-1)d`, where,

`A_n` = nth term of sequence.

a = First term of sequence,

n = Number of terms,

d = Common difference.

1st terms of our given sequence is 13.

`A_n=13+(n-1)13`

`A_n=13+13n-13`

`A_n=13n`

Therefore, the formula of our given sequence is
`A_n=13n`.

Next term of sequence would be
`61+13=74`.

Therefore, the next term of sequence is 74.