Question

The sum of 11 terms of an AP whose 6th term is 5 is _____

a) 40 b) 55 c) 65 d) None of these​

Answer 1

Answer:

Given,

${ \star{ \mathbb{n = 6}}} \\ { \star{ \mathbb{a _{n} = 5}}}$

$a_{n} = a + (n - 1)d \\ 5 = a + (6 - 1)d \\ 5 = a + 5d \\ a = 5 - 5d$

Now to find the sum of 11 terms of the A.P

given,

${ \star{ \mathbb{n = 11}}} \\ { \star{ \mathbb{a = 5 - 5d}}}$

then,

$S_{11} = \frac{11}{2} (2a + (11 - 1)d) \\ S_{11} = \frac{11}{2}(2(5 - 5d) + 10d) \\ S_{11} = \frac{11}{2} (10 - 10d + 10d) \\ S_{11} = \frac{11}{2} \times 10 = 11 \times 5 \\ S_{11} = 55$

So, your answer is 55

Hope it helps you...