Question

Find the sum of all numbers from 50 to 350 which are divisible by 4. Also, find the 15th term.

Answer 1

The numbers from 50 to 350 which are divisible by 4 are

52, 56 , 60, .... 348

It is an A.P. where a = 52 and d = 4

Let t_n = 348

t_n = a+ (n-1)d  

∴ 348 = 52 + (n - 1)(4)

348 - 52 = 4 (n - 1)

`296/4 = "n" -1`

∴ n = 74 + 1

∴ n = 75

`"S"_"n" = "n"/2["t"_1 + "t"_"n"]`

`"S"_25 =25/2 [52 + 348]`

`= 25/2 xx 400`

`"S"_25 = 5000`

∴ The sum of all numbers from 50 to 350 which are divisible by 4 is 5000.

t_n = a + (n - 1)d

∴ t₁₅ = 52 + (15 - 1)(4)

= 52 + 14(4)

= 52 + 56

= 108