Question

Find the 42nd term for the following sequence 6,10,14,18,122

Answer 1

I believe the answer is 174

Answer 2

The 42nd term of the given sequence 6, 10, 14, 18, 122 is 170.

Solution:

The series of number given to us is: 6, 10, 14, 18, 22.

And we have been asked to find the 42nd number of the series.

Firstly, we have figure out what type of series the given numbers form.

If we look closely, we can notice that the difference between consecutive numbers is 4 throughout the given series.

This is the property of arithmetic series.

So, the formula to find the 42nd term of this series is:

`a_(n)=a_(1)+(n-1) d`

`a_n` = the nth term of the sequence

`a_1` = the first term of the series.

n = the number of the term we are looking for

d = the difference between consecutive numbers.

So, on substituting the values in formula we get the following:

`\begin{array}{l}{a_(42)=6+(42-1) 4} \\\\ {a_(42)=6+(41) 4} \\\\ {a_(42)=6+164=170}\end{array}`

Therefore the 42nd term of the given sequence is 170.