Question

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Answer 1

Sum of three numbers in AP is 21

Product of 1st and 3rd number is 45

a, b, c are in sequence

Sum of three numbers

a + b + c = 21

(a+c) + b = 21

2b + b = 21

3b = 21

b = 7

a + 7 + c = 21

a + c = 14

Product of 1st and 3rd number

a × c = 45

quadratic equation formula is

x^2 - ( p + q )x + (p × q) = 0

x^2 - 14x + 45 = 0

x^2 - 5x - 9x + 45 = 0

x(x - 5) - 9 (x - 5) = 0

(x - 5) (x - 9) = 0

x = 5, 9

since,

a = 5, b = 7, c = 9

the common difference = 2

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Answer 2

Answer:

here the 3 term of AP is a-d,a,a+d,

Step-by-step explanation:

so,a-d+a+a+d=21 3a= 21 , so, a = 7 and a-d×a+d= 45 so a²-d²=45 or 49-d²=45 so,d²= 49 -45 so d²= 4 or d= 2 so our 3 number that are in AP a-d=5 ,a=7 and a+d=9 (ans)