Question

Find the wrong term in the sequence: $2,\;5,\;10,\;17,\;26,\;37,\;50,\;64$
(A) $17$
(B) $26$
(C) $37$
(D) $64$

Answer 1

Any arrangement of values in a particular order that is either ascending or descending is said to be a sequence. Since it is mentioned in the question that we are given a sequence, we need to find the pattern that has formed the given sequence. Check if each option satisfies the underlying pattern of the sequence.

Complete step by step solution:
Let us note down the sequence given in the question and observe it carefully;
$2,\;5,\;10,\;17,\;26,\;37,\;50,\;64$
We will try to identify a pattern from the given sequence, for this we look at the terms in the sequence that is correct. The numbers $2,\;5,\,10$ are definitely not wrong terms for this sequence (since they are not given in the options as a possible ‘incorrect term’)
Each of the correct terms ($2,\;5,\,10$) can be expressed in the following manner:
$2 = {1^2} + 1$
$5 = {2^2} + 1$
$10 = {3^2} + 1$
So the pattern for every term or the ${n^{th}}$ term that would be part of the sequence is:
${n^{th}}$ term $= {n^2} + 1$
Now let us look at each option and see if they satisfy the pattern of the sequence, if not then they are the wrong terms in the sequence.
Option (A) $17$ is incorrect, it is part of the sequence. This term $17$ is written as the ${4^{th}}$ term of the sequence. So here $17$ has to be equal to ${4^{^2}} + 1$, and since ${4^{^2}} + 1 = 17$, it means that $17$ is a right term in the sequence and is placed correctly.
Option (B) $26$ is incorrect, it is supposed to be there in the sequence. This term $26$ is written as the ${5^{th}}$ term of the sequence given in the question. So here since ${5^{^2}} + 1 = 26$, it means that $26$ is a correct term within the given sequence so this option is incorrect.
Option (C) $37$ is incorrect, it is there in the sequence. This term $37$ is given as the ${6^{th}}$ term in the sequence in the question. So here since by the pattern of the sequence, ${6^{^2}} + 1 = 37$, it means that $37$ is a right term in the sequence and this option can be rejected.
Option (D) $64$ is correct, since it is the wrong term of the sequence. This term $64$ is given as the ${8^{th}}$ term in the sequence in the question. So here since according to the pattern of the sequence, $64$ should be equal to ${8^{^2}} + 1$. But we know that ${8^{^2}} + 1 = 65$, so $64$ is a wrong term that is placed in the sequence and hence this option is the correct option.
Therefore, the correct pattern is $2,\;5,\;10,\;17,\;26,\;37,\;50,\;65$, so the correct option is option (D) $64$.

Note:
Here we dealt with sequences but there is another term related to sequences which is called series. In a series the terms that are there in an original sequence will be written in a sum form. So if the terms in the sequence are written in a particular order then the sum of all the terms in this sequence is said to be a series.