find five number in AP, whose sum is 35.and the sum of whose squares is 285
Answers
Answer:
3,5,7,9,11 (or) 11,9,7,5,3
Step-by-step explanation:
Let the numbers in AP = a - 2d, a - d, a, a + d, a + 2d.
(i)
Given that Sum is 35.
⇒ a - 2d + a - d + a + a + d + a + 2d = 35
⇒ 5a = 35
⇒ a = 7
(ii)
Sum of whose squares is 285.
⇒ (a - 2d)² + (a - d)² + a² + (a + d)² + (a + 2d)² = 285
⇒ 5a² + 10d² = 285
⇒ 5(7)² + 10d² = 285
⇒ 245 + 10d² = 285
⇒ 10d² = 40
⇒ d² = 4
⇒ d = ±2.
When d = 2:
a - 2d = 7 - 2(2) = 3
a - d = 5
a = 7
a + d = 9
a + 2d = 7 + 2(2) = 11.
When d = -2:
a - 2d = 7 - 2(-2) = 11
a - d = 9
a = 7
a + d = 5
a + 2d = 3.
Therefore, the numbers are : 3,5,7,9,11 (or) 11,9,7,5,3.
Hope it helps!
Step-by-step explanation:
Let five numbers in A.P. be a – 2d, a – d, a, a + d and a + 2d.
Given (a – 2d) + (a – d) + a + (a + d) + (a+ 2d) = 30
Putting a = 6, we get
When a = 6 and d = 2, we get
when a = 6 and d = –2, we get
Five numbers in A.P. are 2, 4, 6, 8 and 10.
Thus, the third number is 6.