The 6th term of an ap is 12 and the 8th is 22, find the 10 th term
Answers
Assume the 1st term to be a, common difference to be d Now, 6th term==> a+(6-1d)=a+5d=12.......(i) Similarly 8th term = a+7d=22.....(ii) Eq. (ii) - (i) a+7d=22 a+5d=12 - - - ---------------- 2d=10 d=5 Now d=5,so a =12-5d=12-10=2 Therefore, 10th term= a+9d=2+9*5=47
Given:
Consider the given AP and conditions are
6th term is 12
8th term is 22
Find:
10th term of AP
Solution:
We know that the nth term of the AP is Tn = a + (n-1) d
where a is th first term and d is the common difference
Therefore
T6 = 12 = a + (6-1)d
a + 5d = 12 ... (1)
T8 = 22 = a + (8-1) d
a + 7d = 22 ...(2)
Subract equation (1) from (2) we have
2d = 10
d = 5
Substitute the value of d inti equation (1) we have
a + 25 = 12
a = -13
Therefore 10th term will be
T10 = a + (n -10)d
T10 = -13 + (10-1)5
T10 = 82
The 10th term will be 82.