Question

Find the next two terms of the sequence. 2,6,10,14,...

Answer 1

The next two terms of the given sequence are $\boxed{\bf 18\text{ and }\bf 22}$ i.e, $\boxed{\bf option C}$

Further explanation:

It is given that the sequence is $2,6,10,14,..$.

A sequence is defined as a serial arrangement of numbers or things which follow a definite order.

For any sequence first we need to find the order in which the sequence is arranged.

The sequence is $2,6,10,14,..$ in which we can see that this sequence is following a definite order that is when we add $4$ in the first term $2$ then we get $6$, when we add $4$ in the second term $6$ then we get $10$.  

Similarly $10$ and $14$ is also following the same pattern that when we add $4$ in previous number we get the next number.

This way we can see that the given sequence is following the pattern that is if we add $4$ in previous number we get the next number.

So the next term of the sequence can be calculated by adding $4$ in the last number that is $14$.

The next term is calculated as follows:

$\boxed{14+4=18}$

Now add $4$ in $18$ to get the next term of the sequence as shown below:

$\boxed{18+4=22}$

Therefore the next two consecuticve terms of the given sequence are $18\text{ and }22$.

In option (A) the next two term are given as $16\text{ and }18$ which is not matching with the above answer.

So the option (A) is incorrect.

In option (B) the next two term are given as $18\text{ and }24$ which is not matching with the above answer.

So the option (B) is also incorrect.

In option (C) the next two term are given as $18\text{ and }22$ which is matching with the above answer.

So the option (C) is correct.

In option (D) the next two term are given as $16\text{ and }20$ which is not matching with the above answer.

So the option (D) is also incorrect.

Thus, the correct option is $\boxed{\bf option C}$.

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Answer details:  

Grade: High School

Subject: Mathematics

Chapter: Sequence and Series

Keywords:  Sequence, series, 2,6,8,10,14... , option (C), 18,22 , terms, order, common difference, arrangement, previous number, following number, matching, definite order.

Answer 2

Answer: Our required two terms will be 18 and 22.

Explanation:

Since we have given that

The sequence : 2,6,10,14........

Here, a = 4

common difference = d is given by

$d=a_2-a_1=6-2=4$

We also have a formula to find the nth term, i.e.

$a_n=a+(n-1)d$

We need to find the next two terms , that is 5th and 6th term

So it will be

$a_5=a+(4-1)d=a+4d=2+4\times 4=2+16=18\\\\a_6=a+(6-1)d=a+5d=2+5\times 4=2+20=22$

Hence , our required two terms will be 18 and 22.