Question

The sum of first 25 terms of an A.P., whose nth term is given by Tn= (7 - 3n) is
(1) - 800
(2) – 850
(3) - 900
(4) - 950​

Answer 1

Step-by-step explanation:

Given:

$t_n= 7-3n \\ \therefore \: \: \: \: t_1= 7-3 \times 1 = 7 - 3 = 4 \\and \: t_2= 7-3 \times 2 = 7 - 6 = 1\\ thus \: a = 4 \\ d = 1 - 4 = - 3 \\ now \\ \because \: s_{n} = \frac{n}{2} \{2a + (n - 1)d \} \\ \therefore \: s_{25} = \frac{25}{2} \{2 \times 4 + (25- 1)( - 3) \} \\ \therefore \: s_{25} = \frac{25}{2} \{8 +24( - 3) \} \\ \therefore \: s_{25} = \frac{25}{2} \{8 - 72 \} \\ \therefore \: s_{25} = \frac{25}{2} \times ( - 64) \\ \therefore \: s_{25} = 25 \times ( - 32) \\ \therefore \: s_{25} = - 800$

Thus, the sum of first 25 terms is - 800.