Question

in an Ap the sum of second and third term is 22, and the product of first and fourth term is 85.Find the first four terms​

Answer 1

I hope it is helpful for you

Answer 2

Answer:

The first 4 terms are 5,9,13 and 17

Step-by-step explanation:

we know, tₙ = a + (n-1)d

Given, t₂ + t₃ = 22

ie,  a+d + (a+2d) = 22

=> 2a+3d = 22  ------------ (1)

( we can say a+a+3d=22

 => a+3d = 22-a )

also, t₁*t₄ = 85

=> a(a+3d) = 85

=> a(22-a) = 85

=> 22a-a²= 85

=> a²-22a+85 = 0

on factorising we have,

(a-17)(a-5) = 0

=> a-17=0  or a-5 = 0

=> a = 17 or a = 5

when a= 17,

(1) => 2(17)+3d = 22

   => 34 + 3d=22

   => 3d = 22-34

   => 3d = -12

   => d = -12/3

   => d = -4

also, when a= 5,

(1) => 2(5)+3d = 22

   => 10 + 3d=22

   => 3d = 22-10

   => 3d = 12

   => d = 12/3

   => d = 4

so, the 4 terms, a, (a+d) , (a+2d) and (a+3d)

(when a= 17 and d=-4)

=> 17, 17+(-4) , 17+2(-4) and 17+3(-4)

=> 17, 17-4 , 17-8 and 17-12

=> 17,13,9 and 5

(when a= 5 and d=4)

=> 5, 5+(4) , 5+2(4) and 5+3(4)

=> 5, 5+4 , 5+8 and 5+12

=> 5,9,13 and 17