The next two terms of the given sequence are i.e,
Further explanation:
It is given that the sequence is .
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 in which we can see that this sequence is following a definite order that is when we add in the first term then we get , when we add in the second term then we get .
Similarly and is also following the same pattern that when we add 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 in previous number we get the next number.
So the next term of the sequence can be calculated by adding in the last number that is .
The next term is calculated as follows:
Now add in to get the next term of the sequence as shown below:
Therefore the next two consecuticve terms of the given sequence are .
In option (A) the next two term are given as which is not matching with the above answer.
So the option (A) is incorrect.
In option (B) the next two term are given as 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 which is matching with the above answer.
So the option (C) is correct.
In option (D) the next two term are given as which is not matching with the above answer.
So the option (D) is also incorrect.
Thus, the correct option is .
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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.