Question

there are 11 terms in an A.P. the value of the middle most term is 30. Find the sum of all terms of this A.P​

Answer 1

Answer:

The sum of all terms of the given A.P. is 330

Step-by-step explanation:

Given :

• There are 11 terms in an A.P.
• The value of the middle most term is 30.

To find :

the sum of all terms of this A.P​

Solution :

The middle term of the given A.P. is 6th term.

Hence, 6th term = 30

nth term of an A.P. is given by,

aₙ = a + (n - 1)d

where

a denotes the first term

d denotes the common difference

Put n = 6,

a₆ = a + (6 - 1)d

30 = a + 5d

Sum of first n terms of an A.P. is given by,

 $\sf S_n=\dfrac{n}{2}[2a+(n-1)d]$

We have to find the sum of 11 terms of the given A.P.

Put n = 11,

 $\sf S_{11}=\dfrac{11}{2}[2a+(11-1)d] \\\\ \sf S_{11}=\dfrac{11}{2}[2a+10d] \\\\ \sf S_{11}=\dfrac{11}{2}[2(a+5d)] \\\\ \sf S_{11}=11(a+5d) \\\\ \sf S_{11}=11(30) \\\\ \sf S_{11}=330$

Therefore, the sum of all terms of the given A.P. is 330