Question

the sum of 2,4,6,8 series numbers of 1 to 50 is 2550 .....then find sum of 1,3,5,7 series in 1 to 50​

Answer 1

Step-by-step explanation:

Given series is: 1, 3, 5, 7,.........,49 which is in AP.

$\therefore \: a = 1 \\ \: \: \: \: \: d = 2 \\ \: \: \: \: \: t_n = 49 \\ \because \: t_n = a + (n - 1)d \\ \therefore \: 49 = 1 + (n - 1) \times 2 \\ \therefore \: 49 - 1 = (n - 1) \times 2 \\ \therefore \: 48 = (n - 1) \times 2\\ \therefore \: \frac{48}{2} = (n - 1)\\ \therefore \: 24 = n - 1 \\ \therefore \: n = 24 + 1 \\ \therefore \: n =25 \\ next \: sum \: of \: ap \\ s_n = \frac{n}{2} (a + t_n) \\ \therefore \: s_{25} = \frac{25}{2} (1 + 49) \\\therefore \: s_{25} = \frac{25}{2} \times 50\\\therefore \: s_{25} = 25\times 25\\\therefore \: s_{25} = 625$