SOLUTION: The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78. Find the sum of the first 30 terms.
Algebra ->
Sequences-and-series
-> SOLUTION: The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78. Find the sum of the first 30 terms.
Log On
Question 998073: The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78. Find the sum of the first 30 terms. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The sum of the first eight terms of an A.P. is 4 and the sum of the first twelve terms is 78. Find the sum of the first 30 terms.
--------
1st 8 terms:: 4[a(1)+a(1)+3d] = 8a(1) + 12d = 4
--------
1st 12 terms: 6[a(1)+a(1)+11d] = 12a(1)+ 66d = 78
--------
Multiply thru the 1st equation by (3/2) to get::
12a(1) + 18d = 6
12a(1) + 66d = 78
-------------
48d = 72
d = 3/2
----
Solve for "a(1)"::
8a(1) + 18d = 4
8a(1) + 27 = 4
-----
8a(1) = -23
a(1) = -23/8
-------
Ans: S(30) = 15[(-23/8) + [-23/8+19(3/2)]] =
Do the arithmetic.
Cheers,
Stan H.
-------------
(