The sum 47

The sum of 3 numbers in an arithmetic progression (AP) is 15. If 1,4,19 are to be added to the above numbers respectively, it formed a geometric progression (GP). Find the numbers.

Correct answer:

a =  2
b =  5
c =  8

Step-by-step explanation:

b=a+D c = b+D  s=15 s=a+b+c=a+(a+D)+(a+2D) s = 3a + 3D  g1=1+a g2=4+b g3 = 19+c  g2=q g1 g3=q g2  15=3a+3D 5= a+D  g2/g1 = g3/g2  (4+b)2 = (1+a) (19+c) (4+a+D)2 = (1+a) (19+a+2D)  (4+a+5a)2 = (1+a) (19+a+2(5a))  92=(1+a) (29a)  92=(1+a) (29a) a228a+52=0  p=1;q=28;r=52 D=q24pr=2824152=576 D>0  a1,2=2pq±D=228±576 a1,2=228±24 a1,2=14±12 a1=26 a2=2  a=a2=2  D=5a=52=3

Our quadratic equation calculator calculates it.

c=b+D=5+3=8   Verifying Solution:   S=a+b+c=2+5+8=15  g1=1+a=1+2=3 g2=4+b=4+5=9 g3=19+c=19+8=27  Q1=g2/g1=9/3=3 Q2=g3/g2=27/9=3

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