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# What is the next number in the sequence 121,126,141,166,201?(a) 206(b) 212(c) 230(d) 246

Last updated date: 14th Jul 2024
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Hint: Firstly, we have to subtract the first term from the second term. Then, we have to subtract the second term from the third and so on. We can write these differences as a sequence and find the common difference of this sequence. Then, we have to add this common difference to the last term of this sequence. Then, we have to add the last term of the given sequence with the result of the previous step.

Complete step by step solution:
We have to find the next number in the sequence 121,126,141,166,201. Let us subtract the first term from the second term.
$\Rightarrow 126-121=5$
Now, we have to subtract the second term from the third.
$\Rightarrow 141-126=15$
Let us subtract the third term from the fourth.
$\Rightarrow 166-141=25$
Now, we have to subtract the fourth term from the fifth.
$\Rightarrow 201-166=35$
We can write the difference in a sequence as shown below.
5, 15, 25, 35
We can see that the common difference between the above sequence is 10. So the difference between the fifth term and the required term will be $35+10=45$ .
Now, we have to add the fifth term, that is, 201 and 45.
Required number $=201+45=246$
Therefore, the next number in the sequence 121,126,141,166,201 is 246. So, the correct answer is “Option (d)”.

Note: Students must always try to find the relation between the terms in the given sequence. This relation can be obtained by subtracting, dividing or multiplying the adjacent terms. In the above solution, students have a chance of making a mistake by subtracting 45 from 201 instead of adding 45 and 201.