Question

If the sum of three consecutive terms of an increasing ap 51 and product of first and third of these terms is 273

Answer 1

Answer:

13, 17, 21

Step-by-step explanation:

let the AP be a-d, a, a+d

sum of the terms is 51

a - d + a + a + d = 51

3a = 51

a = 51/3

a = 17

product of first and third term is = 273

(a - d)(a + d) = 273

${a}^{2} - {d}^{2} = 273 \\ {17}^{2} - {d}^{2} = 273 \\ 289 - {d}^{2} = 273 \\ {d}^{2} = 289 - 273 \\ {d}^{2} = 16 \\ d = \sqrt{16} \\ d = 4$

a = 17 d = 4

the AP is

a - d = 17 - 4 = 13

a = 17

a + d = 17 + 4 = 21

the three numbers are 13, 17, 21

hope you get your answer