The sum of four numbers in arithmetic progression is 16.The square of the last number is the square of the first number plus 48. What is the third number?
----(Maths)
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Answered by
69
Answer:
A+A+d+A+2d+a+3d=16
4A+6d=16
2A+3d=8
(A+3d)^2=A^2+48
second equation...
A^2+6dA+9d^2=a^2+48
3d(2A+3d)=48
3d*8=48
d=2
then 2A+6=8
A=1
1,3,5,7
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Answered by
40
The sum of four numbers in arithmetic progression is 16.The square of the last number is the square of the first number plus 48. What is the third number ❓❓
The four numbers in the AP can be taken as
a - 3d, a - d, a + d and a + 3d.
Given their sum is 16.
=> 4a = 16 => a = 4.
Also given (4 + 3d)² = (4 - 3d)² + 48
=> 16 + 24d + 9d² = 16 - 24 d + 9d² + 48
=> 48 d = 48 => d = 1.
So the numbers are 1, 3, 5, 7
The third term in the sequence is 5
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