The sum of 4 numbers in AP is 32 and
the sum of their squares is 276. Find the
numbers.
Answers
Answer:
Sum = 32
a-3d + a-d + a+d + a+3d 32
4a = 32
.. a = 8
Sum of squares = 276 =
(a-3d)? + (a-d)? + (a+d)? + (a+3d)? =
a? - 6ad + 9d+ a² - 2ad + d + a² + 2 ad + d2 + a? + 6ad + 9d? = 276
4a? + 20d? = 276
a? + 5d? = 69
Substituting a = 8
82 + 5d? = 69
64 + 5d= 69 5d2 = 5 d? = 1
. d = ±1
Numbers are - 5, 7, 9, 11 or 11, 9, 7,5
Step-by-step explanation:
mark me as brainliest answer then I will follow you
Answer:
, 7, 9, 11
Step-by-step explanation:
Let the numbers be a-3d, a-d, a+d, a+3d.
This is an AP which has common difference of 2d.
Sum = 32
a-3d + a-d + a+d + a+3d = 32
4a = 32
∴ a = 8
Sum of squares = 276
(a-3d)² + (a-d)² + (a+d)² + (a+3d)² = 276
a² - 6ad + 9d² + a² - 2ad + d² + a² + 2ad + d² + a² + 6ad + 9d² = 276
4a² + 20d² = 276
a² + 5d² = 69
Substituting a = 8
8² + 5d² = 69
64 + 5d² = 69
5d² = 5
d² = 1
∴ d = ± 1
Numbers are - 5, 7, 9, 11 or 11, 9, 7, 5
Hope this helps! :)
Please mark as brainliest!