Question

how many numbers between 1 and 400 are exactly divisible by 7.​

Answer 1

${\bold{\underline{\underline{Arithmetic \:Progressions}}}}$

The concept of arithmetic progressions shall be applied here.

⚫So , the first number divisible by seven is 1. Therefore our first term (a) becomes 7.

⚫Continuing the series we have ,

${\bold{7 , 14 , 21...........399}}$

This forms an AP with

→first term a = 7

→Common Difference d = 7 (a2 - a1)

→ Last term L = 399

→ Number of terms (n) = ?

✔Using the formula ,

=> L = a + (n-1) d

↪399 = 7 + (n-1)7

↪392/7 = n - 1

↪56 = n - 1

${\sf{\underline{\red{n = 57}}}}$

${\bold{\underline{\underline{Number\:of\:terms\:are\:57 }}}}$