Question

The next two terms of the sequence 5, 18, 31, 44, ....... are: * (i) 49 and 54 (ii) 57 and 70 (iii) 62 and 80 (iv) 75 and 119

Answer 1

Option (ii)

Explanation:

Given :

The sequence 5, 18, 31, 44, ______?

To Find :

The next two terms.

Solution :

The given sequence [ 5, 18, 31, 44 ] is an arithmetic sequence. Because there is a common difference between each term. If you add 13 to the previous term. It will give the next term.

We know that :

$\bigstar\;\boxed{\bf a_n=a_1+d(n-1).}}}$

Hence,

The Arithmetic Sequence: d = 13

Substitute in the values of a₁ = 5  & d = 13.

Simplifying each term by using distributive property,

So,

$\implies \sf a_n=5+13n+13\times-1\\ \\ \\\implies \sf 13\;by -1.\\ \\ \\ \implies \sf a_n=5+13n-13$

Subtract 13 from 5.

$\implies \sf a_n=13_n-8$

Substituting in the value of n to find the term.

$\implies \sf a_6=13(6)-8$

Multiplying 13 by 6.

$\implies \sf a_6=78-8$

Subtracting 8 from 78.

$\implies \sf a_6=70$

The term 57 & 70 was calculated with the same method.