Question

Find out the wrong number in the sequence $7,8,18,57,228,1165,6996$.
A) $8$
B) $18$
C) $57$
D) $228$
E) $1165$

Answer 1

Hint: To find out the wrong number in the given sequence, we will first find out the pattern of the sequences followed and then eventually the wrong number in between the given sequence.

Complete step by step solution:
Let us assume that the given data be: A, B, C, D, E, F
Now, we can observe that the pattern of the sequence is in the way as –
$A,A \times 1 + 1,B \times 2 + 2,C \times 3 + 3,D \times 4 + 4,E \times 5 + 5,F \times 6 + 6$
Place the value of first number A and get the value of B
$
  A = 7 \\
  B = A \times 1 + 1 = 7 \times 1 + 1 = 8 \\
 $
Similarly find the other terms and check the given terms.
\[
  C = B \times 2 + 2 = 8 \times 2 + 2 = 16 + 2 = 18 \\
  D = C \times 3 + 3 = 18 \times 3 + 3 = 54 + 3 = 57 \\
  E = D \times 4 + 4 = 57 \times 4 + 4 = 228 + 4 = 232 \\
  F = E \times 5 + 5 = 232 \times 5 + 5 = 1160 + 5 = 1165 \\
  G = F \times 6 + 6 = 1165 \times 6 + 6 = 6990 + 6 = 6996 \\
 \]
From the above equations, we can identify that the term $282$ is not present and so to follow the pattern $228$ is the wrong number.
Hence, option (D) is the correct answer.

Note:
Always be good in basic four operations that is Division, Multiplication, Addition and the subtraction and use different techniques and ways to identify the correct pattern to know the right and the wrong numbers in the sequence.