Book Online Demo

Check Your IQ

Courses

If the $n^{th}$ term of an AP is $\frac{1}{3} (2 n + 1)$ , then find the sum of its $19$ terms.

see full answer

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

131

132

133

134

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given, the

n^{th}

term of an AP is

\frac{1}{3} (2 n + 1) .

nth term of an A.P is calculated using

a_{n} = a + (n - 1) d .

{\Rightarrow a}_{n} = a + nd - d

Substitute

n = 1,

a_{1} = \frac{1}{3} (2 (1) + 1)

\Rightarrow a_{1} = 1

Substitute

n = 2,

a_{2} = \frac{1}{3} (2 (2) + 1)

\Rightarrow a_{2} = \frac{5}{3}

Now,

d = \frac{5}{3} - 1

\Rightarrow d = \frac{2}{3}

a = 1

.
Sum of first

n

terms

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

S_{19} = \frac{19}{2} [2 + (18) \frac{2}{3}]

{\Rightarrow S}_{19} = \frac{19}{2} [14]

{\Rightarrow S}_{19} = 19 [7]

{\Rightarrow S}_{19} = 133

Hence, the required sum is 133.
Therefore, option 3 is correct.

Watch 3-min video & get full concept clarity