 Hello and welcome to problem solving session on arithmetic progression and we are taking problems which deal with sum of n terms of an AP. Now the given question says if the nth term of an AP is 2 n plus 1, find the sum of first n terms of the AP. Okay, this is what we have to find out. So let's solve this. So if you see this is a mix of our previous knowledge on nth term and the knowledge on the sum of n terms of an AP. So let's write out, write the formula for sum of n terms of an AP. It's nothing but n by 2 a plus n minus 1 d where what a is first term, first term and d is common difference. Correct? Yes, common difference. So now in this case it's given that an nth term is given as 2 n plus 1. So we have to just find out a and d and we are done. So what is a1? The first term will be simply put n equals to 1 and this is 3. And what is common difference d? So for that if you find out a2, it will be helpful. So let's find out a2 first. a2 is 2 into 2 plus 1 which is 5. So d will be nothing but common difference is a2 minus a1 any difference of any two consecutive terms. So that means 5 minus 3 is 2. So clearly we got a as 3 and d as 2. Now we can deploy that in the given formula. So sn is equal to n by 2 for any n. a is 3 plus n minus 1 times. Right? If you simplify this you'll get n by 2 and 3 plus 2n minus 2. Right? So n by 2 into sorry one thing which we missed is this is 2 a. So this is 2 into 3. Correct? So 6 plus 2n minus 2 which is n by 2 2n plus 4. Correct? So if you simplify further you'll get n and you can take out 2 common from the second term. It will become n plus 2. So n into n plus 2 is the sum of nth term. So if you see what will be s10? So sum of first 10 terms will be simply 10 into n plus 2. That is 120. Right? Likewise you can find out s15. Sum of first 15 terms of the given AP will be 15 into 17 15 plus 2. Correct? And it will be 255. Right? So this is how you can find out the sum of any number of terms if the nth term is given.