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

1.	How many numbers between 1 and 400 are exactly divisible by 7.
Answer» ${\bold{\underline{\underline{Arithmetic \:Progressions}}}}$ 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 , ${\bold{7 , 14 , 21...........<klux>399</klux>}}$ 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 ${\sf{\underline{\red{n = 57}}}}$ ${\bold{\underline{\underline{Number\:of\:terms\:are\:57 }}}}$

Answer»

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

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 ,

${\bold{7 , 14 , 21...........<klux>399</klux>}}$

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

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

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

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