The sum of the 1st 8 term of an A.P is 60 and the sum of the next six terms is 108. Find the first term and common difference.
Comments
The sum of the nth term of an ap is given by:
Sn = n/2 (2a + (n - 1)d)
where a is the first term and d is the common difference.
for the first 8th term, S8 = 8/2 (2a + (8 - 1)d) = 60
4 (2a + 7d) = 60
divide both sides by 4
2a + 7d = 15 ---------- eqn(1)
fro the firest 6th term, S6 = 6/2 (2a + (6 - 1)d) = 108
3 (2a + 5d) = 108
divide both sides by 3
2a + 5d = 36 -------------- eqn(2)
eqn(1) and eqn(2) are simultaneous equations and can be solved by elimination method.
Subtract eqn(2) from eqn(1),
(2a - 2a) + (7d - 5d) = 15 - 36
2d = -21
divide both sides by 2
d = -21/2
Substitute d = -21/2 into eqn(1)
2a + 7(-21/2) = 15
2a - 147/2 = 15
add 147/2 to both sides
2a = 15 + 147/2
2a = 177/2
divide both sides by 4
a = 177/4
= 44.25
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