Question

Find the wrong term in sequence: 5, 10, 17, 24, 37, 50, 65.
\[\begin{align}
  & \text{a) 10} \\
 & \text{b) 17} \\
 & \text{c) 24} \\
 & \text{d) }\text{37} \\
 & \text{e) }\text{50} \\
\end{align}\]

Answer 1

Hint: Now we are given the sequence 5, 10, 17, 24, 37, 50, 65. First we will subtract the consecutive terms and form a new sequence made of difference of two consecutive terms. Now this new sequence is in AP. hence we can easily figure out the wrong term in the given sequence.

Complete step by step answer:
Now consider the given sequence 5, 10, 17, 24, 37, 50, 65.
Now let us check the difference between each consecutive term.
10 – 5 = 5
17 – 10 = 7
24 – 17 = 7
37 – 24 = 13
50 – 37 = 13
65 – 50 = 15.
Now let us form a new sequence whose terms are the difference between two consecutive terms.
5, 7, 7, 13, 13, 15
Now if we change this sequence to 5, 7, 9, 11, 13, 15 then we get a proper Arithmetic progression with common difference 2.
Hence we see that there is a mistake in the calculation.
Now let us replace the number 24 by 26.
Then we get the difference as,
10 – 5 = 5
17 – 10 = 7
26 – 17 = 9
37 – 26 = 11
50 – 37 = 13
65 – 50 = 15.
Now we can see that the difference is in proper arithmetic progression 5, 7, 9, 11, 13, 15.
Hence we can say that 24 should be replaced by 26 in the given sequence.
Hence 24 is the wrong term.

So, the correct answer is “Option C”.

Note: Now in the solution we knew that the sequence does not fit in because of two differences 24 – 17 = 7 and 37 – 24 = 13. Now we can see that the common term in both the difference is 24. Hence we know that 24 is the term which should be replaced. Though to confirm the answer just replace the answer and check once. For example let us say we replace 24 by x. To form a proper AP we want x – 17 = 9 hence we get x = 26. Now similarly we want 37 – x = 13.
Hence we have 37 – 13 = x and hence x = 26. This means we were right about replacing 24 by 26.