the 8th term of an AP is 37 and its 12th term is 57. FIND the AP.
Answers
Answer:
a8= a+7d =37 - - - - - - (1)
a12= a+11d=57———(2)
From 1 and 2
a+7d=37
a+11d=57
We get,
4d=20
d=20/4
Therefore d=5
From (1)
a+7d=37
a=37–35
a=2
Therefore we have got the value of a and d
As a=2 and d=5
We know that
a=2
As, a+d=a2
2+5=7
As a+2d=a3
2+5(2)=a3
=2+10
12
Therefore ap= 2,7,12…….
Hope these will help you!
Answer :-
A.P → 7, 12, 17, 22,...
Step-by-step explanation :-
Given:
- 8th term of the A.P is 37
- 12th term of the same A.P is 57
To find:
A.P = ?
Solution:
For the 8th term:
aₙ = a + (n - 1)d
➟ a₈ = a + (8 - 1)d
➪ 37 = a + 7d ----- [Equation ⓵]
For the 12th term:
aₙ = a + (n - 1)d
⇒ a₁₂ = a + (12 - 1)d
⇒ 57 = a + 11d ----- [Equation ⓶]
[Equation 2] - [Equation 1]
57 - 37 = a - a + 11d - 7d
⇒ 20 = 4d
⇒ d = 20/4
⇒ d = 5
Substitute the value of d in any one of the equations to find the value of 'a'
37 = a + 7d
⇒ 37 = a + 7 (5)
⇒ 37 = a + 35
⇒ a = 37 - 35
⇒ a = 2
A.P → (a + d), (a + 2d), (a + 3d),...
∴ A.P → 7, 12, 17, 22,...