Question

Find the sum of 32 terms of an A.P., where 3-4 term is 1 and 6th term is -11.​

Answer 1

Step-by-step explanation:

Hope it helps and

pls mark me branliest

Answer 2

☆ Solution ☆

Given :-

• The Sum of 32 terms of an A.P., where 3-4 term is 1 and 6th term is -11.

To Find :-

• The sum

Step-by-Step-Explaination

Let x be the first terms and y be the common difference.

3rd term = x + ( n -1 ) y

Here n = 3

= x + 2y

3rd term = 1 ....................given

Hence ,

x + 2y = 1 ........................ ( 1 )

6th term = x + ( n - 1 ) y

Here n = 6

= x + 5y

6th term = - 11 .................... ( given )

Hence,

x + 5y = - 11 ........................... ( 2 )

Subtracting equation ( 1 ) from ( 2 )

x + 5y = - 11

- x + 2y = 1

_____________

3y = - 12

$y = \frac{12}{3} = - 4$

Hence,

Putting y = - 4 in equation ( 1 )

x + 2y = 1

x + 2 × ( - 4 ) = 1

x - 8 = 1

x = 9

Sum formula

S ( n ) = $\frac{n}{2}$ [ 2x + ( n -1 ) y ]

Sum of 32 terms

= S ( 32 ) = $\frac{32}{2}$ [ 2 × 9 + ( 32 - 1 ) × ( - 4 ) ]

= 16 [ 18 + 31 × ( - 4 ) ]

= 16 ( 18 - 124 )

= 16 ( - 106 )

= - 1696

Hence,

- 1696 is the answer.