Question

The sum of first n terms of an A.P. is

$\frac{n}{2} (3n + 13)$
Find its 30th term.

Answer 1

I am going to solve the method using Comparison Technique, Here is the solution,

n/2(3n+13) is the sum of first n terms of A.p - GIVEN,

We know that, In general , The sum of first n terms of A.p is n/2(2a+(n-1)d),
Now, Compare both the equations,

=> We will get, 2a+ (n-1)d = 3n+13,
=> 2a + nd - d = 3n + 13,
=> (2a-d) + nd = 3n + 13 (Here it is just comparison, There is nothing to do with = symbol ),

Now we can see that, Using Comparison we can write, 
3n = nd, 
=> d = 3,
And also,

2a -d = 13,
2a-3 = 13,
 a = 8,

Now, we get all the values we need,
Now, Let us find the 30th term,

In general, nth term of A.p is a + (n-1)d,

=> 30th term = a + 29d, substitute all the values,
=> 30th term = 8 + 29*3,
=> 30th term = 8 + 87,
=> 30th term = 95,

So therefore the 30th term of an A.p is 95,

Hope you understand, Have a Great Day !,
Thanking you, Bunti 360 !