the sum of first 8th term of an a.p is 80,and the sum if the next 4terms is 88 determine the a.p
8/2 (2a+7d) = 80
12/2 (2a+11d) = 80+88
Now just solve for a and d
In AP:
an = a + ( n - 1 ) d
where
a = first term
d = common difference
Sum of n terms:
Sn = n [ 2 a + ( n - 1) d ] / 2
In tis case:
n = 8
S8 = 80
8 • ( 2 a + 7 d ) / 2 = 80
4 • ( 2 a + 7 d ) = 80
Divide both sides by 4
2 a + 7 d = 20
The sum of the next 4 terms is 88.
a9 + a10 + a11 + a12 = 88
a + 8 d + a + 9 d + a + 10 d + a + 11 d = 88
4 a + 38 d = 88
Now solve system of 2 equations:
2 a + 7 d = 20
4 a + 38 d = 88
The solution is:
a = 3 , d = 2
Check result.
First 8 term in your AP is:
3 , 5 , 7 , 9 , 11 , 13 , 15 , 17
3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 80
Nex 4 terms are:
19 , 21 , 23 , 25
19 + 21 + 23 + 25 = 88