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If the sum of first n terms of an A.P. is given by $S_n = \frac{n}{2} (3n + 1)$, then the first term of the A.P. is
If the sum of first n terms of an A.P. is given by $S_n = \frac{n}{2} (3n + 1)$, then the
first term of the A.P. is
a) 2
b) 3/2
c) 4
d) 5/2
b) 3/2
c) 4
d) 5/2
This Question has 1 answers.
Given the sum of the first $ \displaystyle n $ terms of an A.P.:
$ \displaystyle S_n = \frac{n}{2} (3n + 1) $
The first term $ \displaystyle a $ is given by:
$ \displaystyle a = S_1 $
Substituting $ \displaystyle n = 1 $ in the given sum formula:
$ \displaystyle S_1 = \frac{1}{2} (3(1) + 1) $
$ \displaystyle = \frac{1}{2} (3 + 1) $
$ \displaystyle = \frac{1}{2} \times 4 $
$ \displaystyle = 2 $
Thus, the first term of the A.P. is $ \displaystyle 2 $.
$ \displaystyle S_n = \frac{n}{2} (3n + 1) $
The first term $ \displaystyle a $ is given by:
$ \displaystyle a = S_1 $
Substituting $ \displaystyle n = 1 $ in the given sum formula:
$ \displaystyle S_1 = \frac{1}{2} (3(1) + 1) $
$ \displaystyle = \frac{1}{2} (3 + 1) $
$ \displaystyle = \frac{1}{2} \times 4 $
$ \displaystyle = 2 $
Thus, the first term of the A.P. is $ \displaystyle 2 $.
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