We are given that the fifth term of the arithmetic progression is 18 and the tenth term is -2.
Let's denote the common difference as d.
The fifth term can be expressed as:
a + 4d = 18
The tenth term can be expressed as:
a + 9d = -2
We can subtract the first equation from the second equation to eliminate a:
(a + 9d) - (a + 4d) = -2 - 18
5d = -20
d = -4
Now we can substitute the value of d into either equation to find a:
a + 4(-4) = 18
a - 16 = 18
a = 34
The arithmetic progression is -4, -8, -12, -16, -20, ...
To determine the last term that must be added together so that the progression is negative, we need to find the positive term immediately before it. We can do this by finding the positive term that is closest to zero.
Since the common difference is negative, the progression is decreasing. The progression becomes negative starting from the first term that is less than zero, which is -20. The term before -20 is -16.
Therefore, the last term that must be added together so that the progression is negative is -16.
The fifth and tenth term of arithmetic progression are 18 and -2 find common difference and determine last number of term that must be added together so that progression is negative
1 answer