Q - 60 | CAT Sequence and series Question | 200 Most Important Quant Questions for CAT 2026

[00:00:00]Let's look at this question. This question says there are 10 series and the sum is given by S1, S2, S3 up to and this 10 series consists of 12 terms.

[00:00:13]Right?

[00:00:14]Whose first term is 1, 2, 3 and so on and the common difference is also given to us and we have to find out the sum of all these 10 series. Right?

[00:00:23]So, let's uh first try to form the series. So, if I talk about this, A is 1, D is 1.

[00:00:32]Right? So, series will look like something 1, 2, 3 and so on.

[00:00:37]But, I do not need to make all the series. I can directly say that S1 is basically sum of that series whose first term is 1 and the common difference is 1 and the number of terms is 12. Right? So, we know the formula for the sum is n by 2, so 12 by 2, 2 into A plus n minus 1. If you observe, n minus 1 will be 11 because number of terms is 12. So, 12 minus 1 11. 11 into 1.

[00:01:09]That will be S1.

[00:01:11]In the same way, if I talk about S2, S2, the number of terms is 12 only, but the first term here will be 2.

[00:01:20]And the common difference will be 3.

[00:01:26]Similarly, if I talk about S3, 12 by 2, first term will be 3 and the common difference will be 5.

[00:01:37]Right? So, I'm using this formula, guys.

[00:01:39]Sn is equal to n by 2 2a plus n minus 1 into d.

[00:01:48]Okay. And so on.

[00:01:50]S10, if I ask you, you will simply say 12 by 2, 2 into 10 plus 11 into 19.

[00:01:59]Right?

[00:02:00]Okay. Now, we have to take the sum of all these 10 series.

[00:02:04]Because here it is clearly written summation of SI. It means S1 plus S2 plus S3 dot dot dot S10.

[00:02:16]Right?

[00:02:17]Now, when I try to take the sum, I can see 12 by 2 will come common.

[00:02:25]If I focus on 2, I can say 2 into 1, 2 into 2 2 into 3 dot dot dot 2 into 10 plus similarly 11 into 1, 11 into 3 dot dot dot 11 into 19.

[00:02:44]Now, if you observe 12 by 2 I can write it as 6.

[00:02:49]Here, if I focus, I can take two common.

[00:02:52]It will be 1 plus 2 plus dot dot dot 10.

[00:02:56]If I take 11 common, I will get 1 plus 3 plus 5 dot dot dot 19.

[00:03:05]Right?

[00:03:07]This is sum of n natural number, which is n into n plus 1 by 2.

[00:03:13]So, this will be 2 uh 10 into 11 by 2 I think 55.

[00:03:20]Plus 11 into These are 10 odd numbers, the first 10 odd numbers. And the sum of odd numbers is n squared.

[00:03:30]Sum of odd numbers is n squared.

[00:03:34]Where n is number of terms, right? So, here I can see first 10 odd terms.

[00:03:40]Remember, this formula is for first.

[00:03:44]So, there are 10 odd terms, so I can say directly the sum will be 10 squared.

[00:03:51]Okay, so 6 This will be 110, 1,100.

[00:03:56]6 into 1210 7260. So, answer will be option number D.