Five positive integers are in Ap . the sum of middle 3 terms is 24 and product of first and 5th term 48 find the terms of an Ap.
Answers
Answer:
AP:- -4,-6,8,10,12
Step-by-step explanation:
Five terms in an AP = (a-2d),(a-d),(a),(a+d),(a+2d)
According to given condition
(a-d)+(a)+(a+d)=24 ................................Eq.1
(a-2d) x (a+2d)=48 ...............................Eq.2
Solving equation 1
(a-d)+(a)+(a+d)=24
a+a+a+d-d = 24
3a=24
a=8
Solving equation 2
(a-2d) x (a+2d)=48
(8-2d) x (8+2d)=48
(8²) - (2d)²=48
64 - 4d²=48
-4d²= -16
4d²=16
d²=4
d=√4
d=2
Five terms in an AP = (a-2d),(a-d),(a),(a+d),(a+2d)
a-2d= -4
a-d= -6
a= 8
a+d= 10
a+2d=12
AP:- -4,-6,8,10,12
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Answer:
Answer:-
Given:
Sum of 8th & 4th terms of an AP = 24
Sum of 6th & 10th terms = 44
We know that,
nth term of an AP = a + (n - 1)d
Hence,
⟹ a + (8 - 1)d + a + (4 - 1)d = 24
⟹ a + 7d + a + 3d = 24
⟹ 2a + 10d = 24 -- equation (1)
Similarly,
⟹ a + 5d + a + 9d = 44
⟹ 2a + 14d = 44 -- equation (2)
Subtract equation (1) from (2).
⟹ 2a + 14d - (2a + 10d) = 44 - 24
⟹ 2a + 14d - 2a - 10d = 20
⟹ 4d = 20
⟹ d = 20/4
⟹ d = 5
Substitute the value of d in equation (1).
⟹ 2a + 10(5) = 24
⟹ 2a = 24 - 50
⟹ 2a = 24 - 50
⟹ 2a = - 26
⟹ a = - 26/2
⟹ a = - 13
We know,
General form of an AP is a , a + d , a + 2d...
Hence,
⟹ required AP = - 13 , - 13 + 5 , - 13 + 2(5)...
⟹ required AP = - 13 , - 8 , - 3....