If 8th term of an A.P is 15, then what is the sum of 15 terms?

We are given that

a_{8} = 15

We know that

n^{th}

term of an AP is given as,

t_{n} = a + (n - 1) d

.
So, we get

a_{8} = a + 7 d

a + 7 d = 15

[1]
We know that sum of first n terms of an AP is given as,

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

So, the sum of first 15 terms will be,

S_{15} = \frac{n}{2} [2 a_{1} + (15 - 1) d]

{\Rightarrow S}_{15} = \frac{15}{2} [2 a_{1} + 14 d]

{\Rightarrow S}_{15} = 15 (a + 7 d)

{\Rightarrow S}_{15} = 15 (15)

[from 1]

{\Rightarrow S}_{15} = 225

Therefore, the sum of 15 terms of the AP is 225.
Hence, the correct option is 3.

If $8^{th}$ term of an A.P is $15$ , then what is the sum of $15$ terms?