Question

Find the next term of the series 23, 27, 43, 79, 143, …...
A. 244
B. 243
C. 242
D. 241

Answer 1

Hint: This question is based on logical reasoning. To answer this question, we need to carefully notice and try to observe a sense of pattern in the given series or sequence of numbers. Once we are able to decode this, we can write the next term of the series easily. For the given question, we need to take the differences of the consecutive terms and we can find a pattern in these differences. Implementing the same for the last term in the given question, we can obtain the next term in the sequence.

Complete step by step solution:
This type of question given is called a logical reasoning question. These questions measure the ability of a person to reason out anything logically. It improves the skills of the individual such as interpretation of patterns, decoding number sequences, etc. For the given number sequence question, we are required to find the next term in the sequence. In order to do so, we first subtract each of the terms with the next consecutive term.
For the first pair of numbers 23 and 27,
$\Rightarrow 27-23=4$
Next, we take the second pair of numbers 27 and 43.
$\Rightarrow 43-27=16$
Next, we take the third pair of numbers, 43 and 79.
$\Rightarrow 79-43=36$
Next, we take the fourth pair of numbers, 79 and 143.
$\Rightarrow 143-79=64$
We can see a pattern in this set of numbers 4, 16, 36, 64. The difference between the consecutive numbers are nothing but the squares of even numbers.
Square of 2 is 4.
$\Rightarrow {{2}^{2}}=4$
Square of 4 is 16.
$\Rightarrow {{4}^{2}}=16$
Square of 6 is 36.
$\Rightarrow {{6}^{2}}=36$
Square of 8 is 64.
$\Rightarrow {{8}^{2}}=64$
Therefore, in this series of even numbers, the next even number has to be 10. The square of this number is given as:
$\Rightarrow {{10}^{2}}=100$
This is nothing but the difference between the next term in the series and the last term in the series 143. Let us assume the next term in the series is x.
$\Rightarrow x-143=100$
Therefore, taking 143 to the right-hand side of the equation,
$\Rightarrow x=100+143$
$\Rightarrow x=243$
Hence, the next term in the series is given as 243 which is option B.

Note: Students need to practice more of such logic reasoning questions in order to improve their logic reasoning ability. We need to take care while solving such questions since the answer is not got in one specific method all the time. We need to apply different approaches and based on the hit and trial method; we get a specific method that works for the given question.