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  • The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.  

The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.

 

Answers (1)

Met 1st three terms of AP be \mathrm{(a - d), \ a \ \text{and } (a +d)}

So,    \mathrm{a - d + a + a + d = 18}

          \mathrm{\Rightarrow a = 6}

            \mathrm{(a-d)(a+d) = 5d}

       \mathrm{\Rightarrow a^2 - d^2 = 5d}

       or   \mathrm{d^2 + 5d - 36 = 0}

              \mathrm{(d + 9 )(d-4) = 0}

               \mathrm{d = -9 \ or \ 4}

For d = 4, three numbers are 2,6, and 10

for d = -9, three numbers are 15, 6 and 3

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