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)

${\displaystyle \frac{296}{4}=\text{n}-1}$

∴ n = 74 + 1

∴ n = 75

${\displaystyle {\text{S}}_{\text{n}}=\frac{\text{n}}{2}[{\text{t}}_1+{\text{t}}_{\text{n}}]}$

${\displaystyle {\text{S}}_{25}=\frac{25}{2}[52+348]}$

${\displaystyle =\frac{25}{2}\times 400}$

${\displaystyle {\text{S}}_{25}=5000}$

∴ 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