The 5th term of AP is 20and the 8th term is 32
Answers
Step-by-step explanation:
Let first term and the common difference of the AP be 'a' and 'd' respectively.
So, the 5th term of the AP = a + 4d
and 8th term of the AP = a +7d
A/Q
a + 4d = 20 -------------(1)
and a + 7d = 32 -------------(2)
Now, (2) - (1)=> 3d = 12
=> d = 13÷ 3
So, d = 4
putting d=4 in (1) we get
a + 4×4 = 20
=> a + 16 = 20
=> a = 20- 16
So, a =4
Hence the AP is a , (a+d), (a+3d) , (a+4d) •••••••••••
i.e 4,8,12,16, 20, 24, ••••••••••••
a= 4
d=4
The AP is 4, 8, 12, 16, 20, 24, 28, 32
Explanation:
Given:
1. The 5th term of AP is 20
2. the 8th term is 32
To find:
The first term and Difference
Formula:
First-term = a
Second term = a+d
Third term = a+2d
Fourth term = a+3d
Fifth term = a+4d
Sixth term = a+5d
Seventh term = a+6d
Eight term = a+7d
Solution:
==> The given values are 5th term of AP is 20and the 8th term is 32
==> Fifth term = a+4d
==> Eight term = a+7d
==> Fifth term = 20
==> Eight term = 32
==> 20 = a+4d ==> 1
==> 32 = a+7d ==> 2
using the Elimination method,
==> Multiply by -1 in equation 1
==> a+4d = 20
==> -1(a+4d=20)
==> -a-4d=-20 ==>3
==> Equating equation 2 and 3
==> -a-4d=-20
==> a+7d= 32
-----------------
3d= 12
-----------------
==> 3d =12
==> d = 12÷3
==> d = 4
==> Substitute the d value in equation 1
==> a+4d=20
==> a+4(4)=20
==> a+16=20
==> a=20-16
==> a=4
==> Apply the a and d value in the formula
==> First-term = 4
==> Second term = 4+4
==> Second term = 8
==> Third term = 4+2(4)
==> Third term = 4+8
==> Third term = 12
==> Fourth term = 4+3(4)
==> Fourth term = 4+12
==> Fourth term = 16
==> Fifth term = 4+4(4)
==> Fifth term = 4+16
==> Fifth term = 20
==> Sixth term = 4+5(4)
==> Sixth term = 4+20
==> Sixth term = 24
==> Seventh term = 4+6(4)
==> Seventh term = 4+24
==> Seventh term = 28
==> Eight term = 4+7(4)
==> Eight term = 4+28
==> Eight term = 32
The AP is 4, 8, 12, 16, 20, 24, 28, 32