Question

the sum of three consecutive number of an artimetic progression is30 and their product is 510 find the number​

Answer 1

Step-by-step explanation:

hope it helps..........

Answer 2

GivEn :-

• The sum of three consecutive numbers of an Ap is 30

• The product of three Numbers = 510

To FinD :-

• The Numbers or the Ap

CalculaTioN :-

In an Ap the difference of each term is constant and hence the Common difference d = same all throughout.

Let us Consider the Numbers,

$\sf{(a - d) \: a \: and \: (a + d)}{} \\ \\ \sf{the \: sum \: of \: no = 30}{} \\ \\ \sf{a - d + a + a + d = 30}{} \\ \\ \sf{3a = 30}{} \\ \\ \bold{ \red{hence \: a \: = 10}{} }{}$

It is also Given that the priduct of Numbers = 360

$\sf{(a - d)(a)(a + d) = 510}{} \\ \\ \sf{a( {a}^{2} - {d}^{2}) = 510 }{} \\ \\ \sf{10(100 - {d}^{2}) = 510 }{} \\ \\ \sf{100 - {d}^{2} = 51 } (simplified) \\ \\ \sf{ {d}^{2} = 100 - 51 }{} \\ \\ \sf{ {d}^{2} = 49 }{} \\ \\ \bold{ \red{hence \: d = 7}{} }{}$

Hence Substituting the value of a and d

The Numbers are :-

$\sf{( 10-7) \: (10) \: (10+7)}{} \\ \\ \boxed{ \bold{ \red{★Hence \: Ap = 3,\: 10, \: 17}{} }{} }{}$