30. Find the sum of p terms of that A. P. of which nth term is 3n - 1.
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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,
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,
We have to find the sum of p terms.
So, put n = p and substitute the values of a and d
Therefore, the sum of p terms of the A.P. is (3p² + p)/2
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