Question

The sum of four consecutive terms of an ap is the sum of the third and fourth terms is 11 find the terms​

Answer 1

Answer:

Given:-

Sum of 4 consecutive numbers of an AP

is 2.

Sum of the 3rd and 4th term is 11.

To Find:-

The terms

Solution:-

Define x:

Let the first term be a

First term = a

Second =a+d

Third term = a + 2d

Fourth term = a +3d

Form the equations:-

Sum of 4 consecutive numbers of an AP

is 2.

a +(a + d) + (a +2d) + (a + 3d) = 2

4a +6d =2

2a +3d =1-------------[1]

Sum of the 3rd and 4th term is 11

(a+2d)+ (a + 3d) = 11

2a +5d = 11---------------[2]

[2]-[1]:

2d = 10

d =5

Sub d=5 into [ 1]

2a +3(5)=1

2a +15 1

2a = -14

a = -7

Find the terms:-

First term =a

First ternm=-7

Second term = a +d

Second term= -7+5

Second term = -2

third term = a + 2d

third term =-7+2(5)

third term = 3

Fourth term = a +3d

Fourth term = -7 +3(5)

Fourth term = 8

Answer: The terms are -7, -2, 3 and 8.