Answer:
The explicit formula for the AP is -2n + 3.
1, -1 , -3, -5, -7, -9.........
Step-by-step explanation:
The sum of the first n terms = n/2 [2a1 + (n - 1)d] where a1=first term and d=common difference.
So n10 = 10/2( 2a1 + (10 - 1)d] = -80
n10 = 5(2a1 + 9d) = -80
The sum of 20 terms = -80 + -280 = -360.
So n20 = 20/2(2a1 + (20 - 1)d] = -360
n20 = 10(2a1 + 19d) = -360
Simplifying we have the systems
10a1 + 45d = -80 ...............(1)
20a1 + 190d = -360..............(2)
Multiplying the first equation by 2:
20a1 + 90d = -160..............(3)
Subtract (2) - (3):
100d = -200
d = -2.
and From equation (1):
10a1 = (-80 -(45)*-2) = 10
so a1 = 1.
The explicit formula is 1 + (n - 1)-2
= -2n + 3.
