The sum of 3rd and 5th term of an ap is 16 and their product is 60.find the terms of the ap?
1 Answer
OR
Explanation:
In an arithmetic progression, we add a common difference to each term to get the next term. Therefore,
#t_3 + 2d = t_5#
Letting
#x+ 2d = t_5#
Now we can write down a system of equations
#{(x+ 2d + x = 16), (x(x + 2d) = 60):}#
We simplify the first equation to
This means that
#x(x + 2(8 - x)) = 60#
#x(x + 16 - 2x) = 60#
#x(16 - x) = 60#
#16x - x^2 = 60#
#0 = x^2 - 16x + 60#
#0 = (x- 10)(x - 6)#
#x =10 or 6#
We have a couple of different answers here. If
The terms of the arithmetic progression are therefore:
#6, 10#
It works out to be the same thing if
Hopefully this helps!