Brainly.in What is your question? 1 Primary SchoolMath 5 points Find four numbers in A.P such that the sum of 2nd and 3rd terms is 22 and the product of 1st and 4th terms is 85.
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Let the first term and common difference of the A.P be a and d respectively.
Let the four terms be (a-3d),(a-d),(a+d),(a+3d)
Therefore, A/Q,
(a-d)+(a+d)=22
a-d+a+d=22
2a=22
a=11
Also,
(a-3d)(a+3d)=85
a2-9d2=85
(11)2-9d2=85
121-9d2=85
-9d2=85-121
-9d2=-36
d2=4
d=+-2
Therefore, when a=11,d=2
The four number s are=5,9,13,17
and, when a =11,d =-2
The four numbers are= 17,13,9,5
Let the four terms be (a-3d),(a-d),(a+d),(a+3d)
Therefore, A/Q,
(a-d)+(a+d)=22
a-d+a+d=22
2a=22
a=11
Also,
(a-3d)(a+3d)=85
a2-9d2=85
(11)2-9d2=85
121-9d2=85
-9d2=85-121
-9d2=-36
d2=4
d=+-2
Therefore, when a=11,d=2
The four number s are=5,9,13,17
and, when a =11,d =-2
The four numbers are= 17,13,9,5
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