Math, asked by nandinirana2002, 4 months ago

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

Answers

Answered by snehitha2
3

Answer :

The required sum of p terms of the A.P. is (3p² + p)/2

Step-by-step explanation :

Given :

The nth term of an A.P. is given by (3n - 1)

To find :

the sum of p terms

Solution :

 nth term of an A.P. is given by,

  \underline{\boxed{\bf a_n=a+(n-1)d}}

where

a denotes the first term

d denotes the common difference

nth term = 3n - 1

First term : a = 3(1) - 1 = 3 - 1 = 2

Second term : a₂ = 3(2) - 1 = 6 - 1 = 5

Third term : a₃ = 3(3) - 1 = 9 - 1 = 8

Common difference : d = 5 - 2 = 8 - 5 = 3

Sum of n terms of A.P is given by,

  \underline{\boxed{\bf S_n=\dfrac{n}{2}[2a+(n-1)d]}}

We have to find the sum of p terms.

So, put n = p and substitute the values of a and d

\tt S_p=\dfrac{p}{2}[2a+(p-1)d] \\\\ \tt S_p=\dfrac{p}{2}[2(2)+(p-1)(3)] \\\\ \tt S_p=\dfrac{p}{2}[4+3p-3] \\\\ \tt S_p=\dfrac{p}{2}[3p+1] \\\\ \tt S_p=\dfrac{3p^2+p}{2}

 

Therefore, the sum of p terms of the A.P. is (3p² + p)/2

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