5 terms are in A.P.Sum of middle 3 terms is 24.Product of the first and the 5th is 48.find the terms.?
1 Answer
Explanation:
The nth term of an AP is given by:
And the sum is given by:
Where
If we find the sum of the first 4 terms and subtract the 1st term from this, we will have the sum of the 3 middle terms.
Product of 1st and 5th terms:
We now need to solve our 2 equations simultaneously:
From [1]
Substituting in [2]
Using in [1]:
So we have 2 sets:
Test:
1st term x 5 term = 48
Sum of middle 3 terms:
So there are 2 AP's that meet the conditions: