Do we need to find everything first?
Algebra
Level
2
If the fifth and the fifteenth terms of an arithmetic progression are 20 and -20 respectively, which term of this arithmetic progression is zero?
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1 solution
Let the A.P be a , a + d , a + 2 d , … where a is the first term and d is the common difference.
We have a + 4 d = 2 0 ...(1) and a + 1 4 d = − 2 0 ...(2).
Subtracting equation (1) from (2) we get 1 0 d = − 4 0 or d = − 4 .
Now substitute this value into either of the equations and solve for a . We get a = 3 6 .
Now, we want to find a n such that a + ( n − 1 ) d = 0 or 3 6 + ( n − 1 ) ( − 4 ) = 0 or 3 6 + 4 − 4 n = 0 or n = 1 0 .
Therefore the 10th term of the A.P. is 0 .