Question

Four terms are in AP the sum of extremes is 10 and the product of the means is 24 find the numbers

Answer 1

Answer:

so required APs are

(1) 2,4,6,8

(2) 8,6,4,2

Step-by-step explanation:

a-3d, a-d, a+d, a+2d are 4 terms of AP

Sum of extremes = 10

a-3d+a+3d=10

2a=10

a=10/2

a=5

product of middle two terms= 24

(a-d) (a+d) = 24

a^2-d^2= 24

5^2-d^2= 24

25-24= d^2

d= +1 or -1

if d=1

then the numbers are 5-3(1) =5-3= 2

5-(1) =4

5+1(1)= 5+1 = 6

5+3(1) = 5+3=8

if d= -1

then the numbers are 5-3(-1) =5+3= 8

5-(-1) =5+1 = 6

5+1-(1)= 5-1 = 4

5+3(-1) = 5-3=2

so required APs are

(1) 2,4,6,8

(2) 8,6,4,2