Question

The first term of an ap is 5. The last term is 45 and the sum is 400 then the fourth term apis

Answer 1

Answer:

4th term is 13

Step-by-step explanation:

a = 5

last term = a + (n-1)d = 45

5 + (n-1)d = 45

(n-1)d = 45 - 5

(n-1)d = 40

sum of all terms = Sn = 400

$400 = \frac{n}{2} (2a + (n - 1)d) \\ 400 = \frac{n}{2} (2(5) + (n - 1)d) \\ 800 = n(10 + 40) \: \: \: since\: \: \: \: \: (n - 1)d = 40 \\ 800 = 50n \\ n = \frac{800}{50} = 16$

substitute n in last term

An = 45 =

$5 + (16 - 1)d = 45 \\ 15d = 45 - 5 \\ d = \frac{40}{15} = \frac{8}{3}$

4th term

$= a + 3d \\ = 5 + 3( \frac{8}{3} ) \\ = 5 + 8 \\ = 13$