Grade 11 Arithmetic Series Help?
The Sum of the first 12 terms of an arithmetic series is 186, and the 20th term is 83. What is the sum of the first 40 terms?
Could you please show which equation you used, and how you solved it? (Show all working please)
Thanks.
More Questions From This User See All
Answers & Comments
Verified answer
(1) General arithmetic series : S = a + (a + d) + (a + 2d) + ... + [a + (n - 1)d].
(2) The n(th) term is : a + (n - 1)d
(3) The compact formula for the sum is : S = (n/2)[2a + (n - 1)d]
For your problem, first use (3) with n = 12.
The equation will be : S = (12/2)[2a + (12 - 1)d] = 186,
which can be simplified to 2a + 11d = 31.
Then use (2) with n = 20.
The equation will be : 83 = a + (20 - 1)d,
which is simplified to a + 19d = 83.
Now you have 2 simultaneous equations to solve for 'a' and 'd',
which I'll leave to you to check.
2a + 11d = 31
a + 19d = 83
The answers are : a = -12 and d = 5.
Then use (3) again with n = 40.
The equation will be : S = (40/2)[2*(-12) + (40 - 1)*5],
so, S = 3420.