Question

Find the sum of p terms of that A. P. of which nth term is 3n - 1.​

Answer 1

Answer:

When you have a sum you don't know, some times it's easier to split the sum up into manageable parts.

So let's look at this sum.

sum n=1->p (3n-1)

When dealing with these sums, remember that the associative, distributive, and commutative laws still apply.

So first:

sum n=1->p (3n) - sum n=1->p (1)

Now we can treat this like 2 separate sums. The second is easy.

sum n=1->p (3n) - p

As for the first, there is a trick we can do.

3 (sum n=1->p (n)) - p

Ah… now that's an easy sum and one we already know!

(3(p)(p+1)/2) - p

But we can do better.

(3p+3)(p)/2 - p

((3p+3)p - 2p)/2

(3p+1)p/2