Question

The sum of the first 5 terms of an AP is 50 and that of next 3 is 66. Find the Arithmetic Progression

Answer 1

4,7,10,13,16,19,22,25

because let us assume:
a-2d,a-d,a,a+d,a+2d are in athematic progression.
Given sum of them is 50, and sum of next three numbers (a+3d,a+4d,a+5d) is 66. Solve by this data

Answer 2

Define a:

Let the first number be "a"

The next 4 numbers are (a + d), ( a + 2d), (a + 3d) and ( a + 4d)

Form 1st equation:

a + (a + d) + ( a + 2d) + (a + 3d) + ( a + 4d) = 50

a + a + d +  a + 2d + a + 3d + a + 4d = 50

5a + 10d = 50

a + 2d = 10

Form 2nd equation:

(a + 5d) + (a + 6d) + (a + 7d) = 66

a + 5d + a + 6d + a + 7d = 66

3a + 18d = 66

a + 6d = 22

Putting the 2 equations together:

a + 2d = 10 --------------------- [ 1 ]

a + 6d = 22 --------------------- [ 2 ]

[ 2 ] - [ 1 ] :

4d = 12

d = 12 ÷ 4

d = 3

Sub d = 3 into [ 1 ]

a + 2(3) = 10

a + 6 = 10

a = 10 - 6

a = 4

Form the  Arithmetic Progression (AP):

an = a1 + (n - 1) d

an = 4 + (n - 1)3

an = 4 + 3n - 3

an = 3n + 1

Answer: The AP is an = 3n + 1