Question

find three numbers between 17 and 27 such that they are in A P with 17 and 27​

Answer 1

a = 17

The fifth number is 27.

By using formula ,

$\sf \: t_{n} = a + (n - 1)d$

$\sf \therefore t_{5} = 17 + (5 - 1)d$

$\sf \therefore \:27 = 17 + 4d$

$\sf \therefore 4d = 27 - 17$

$\sf \therefore \: 4d = 10$

$\sf \therefore\: d = \dfrac{10}{4}$

$\sf \implies \: d = 2.5$

Therefore,

$\sf \: t_{2} = t_{1} + d = 17 + 2.5 = 19.5$

$\sf t_{3} = t_{2} + d = 19.5 + 2.5 = 22$

$\sf t_{4} = t_{3} + d = 22 + 2.5 = 24.5$

Therefore, the AP is 17, 19.5 , 22, 24.5, 27.........