Find the 3rd term of an A.P. If the sum of its 5 terms is 60.Choices:- 10 12 14 16
Question
Find the 3rd term of an A.P. If the sum of its 5 terms is 60.Choices:- 10 12 14 16
Solution
To find the 3rd term of an arithmetic progression (A.P.), we first need to understand the formula for the sum of an A.P.
The sum S of n terms of an A.P. with first term a and common difference d is given by the formula:
S = n/2 [2a + (n-1)d]
We know that the sum of the first 5 terms is 60. So, we can write the equation as:
60 = 5/2 [2a + (5-1)d]
Solving this equation, we get:
60 = 5/2 [2a + 4d]
Simplify to get:
24 = 2a + 4d
Divide through by 2 to get:
12 = a + 2d -----(1)
We also know that the third term of an A.P. is given by a + 2d.
From equation (1), we can see that the third term is 12.
So, the answer is 12.
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