Question

Find the wrong term in the sequence :11, 21, 43, 85, 171, 343.
A) 21
B) 85
C) 171
D) 343

Answer 1

Hint:
In the given question, we have been given a sequence of six numbers. We have to find the number which is out of the pattern of the given sequence. For doing that, we are going to write the given numbers and then we are going to pen the sequence they are following.

Complete Step by Step Solution:
$1^{\text{st}}$ number, \[{a_1} = 11\]
$2^{\text{st}}$ number, \[{a_2} = 21\]
Let’s first see the relation between \[{a_1}\] and \[{a_2}\].
\[{a_2} = 2 \times {a_1} - 1\]
Now, 3rd number, \[{a_3} = 43\]
Now, let us see the relation between \[{a_2}\] and \[{a_3}\].
\[{a_3} = 2 \times {a_2} + 1\]
Hence, we can say that for an even positioned term,
\[{a_{2n}} = 2{a_{2n - 1}} - 1\]
and for an odd positioned term,
\[{a_{2n + 1}} = 2{a_{2n}} + 1\]
Following this rule, \[{a_4} = 2 \times {a_3} - 1 = 2 \times 43 - 1 = 85\], which the sequence is following.
Then, \[{a_5} = 2{a_4} + 1 = 2 \times 85 + 1 = 171\], which the sequence is following.
And, \[{a_6} = 2 \times {a_5} - 1 = 2 \times 171 - 1 = 341\], which the sequence is not following.
Hence, the wrong term is \[343\].

Thus, the correct option is (D).

Note:
In finding the answers to the questions involving finding the odd term out, we first write down the relation between the first two terms. Then we write down the relation between the second and the third term. Then we find what is being repeated or changed in the two relations, and then we use the information to find for the odd term. An odd term is the one which does not follow the norms with which the pattern is being governed.