Question

Sum of three nos in ap is 45 and product is 3135 then common difference is

Answer 1

$\underline{\bold{Solution\:-}}$

Let, the three numbers are a-d , a and a+d.

Sum of three numbers is 45

$a - d + a + a + d = 45 \\ \\ 3a = 45 \\ \\ a = \frac{45}{3} \\ \\ a = 15$

Product of these numbers is 3135

$(a - d)a(a + d) = 3135 \\ \\ a( {a}^{2} - {d}^{2} ) = 3135 \\ \\ on \: putting \: value \: of \: a \\ \\ 15( {15}^{2} - {d}^{2} ) = 3135 \\ \\ 225 - {d}^{2} = \frac{3135}{15 } \\ \\ 225 - {d}^{2} = 209 \\ \\ {d}^{2} = 225 - 209 \\ \\ {d}^{2} = 16$

d = ±4

So, there common difference is ± 4.

Additional information:-

A.P. is 15 , 19 , 23 ,.... or. 15, 11 , 7 and so on.

Answer 2

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