Question

the sum of four consecutive terms of an ap is 2. the sum of the third and fourth term is 11 .
find the terms

Answer 1

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Answer 2

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 term = -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