Question

How many multiples of 7 lie between 50 and 250.

Answer 1

$\huge\underline{\bf \orange{Solution :}}$

Multiple of 7 between 50 and 250 are :

→ 7 , 14 , 21 ,......... , 245

By using A.P formula

$\large\implies \boxed { \tt A_n = a + (n - 1)d}$

Here

• a = 7
• d = 7
• Aₙ = 245

Substitute values in formula

$\implies \tt245 = 7 + (n - 1)7 \\ \\ \implies \tt245 - 7 = (n - 1)7 \\ \\ \implies \tt238 = (n - 1)7 \\ \\ \implies \tt \frac{238}{7} = n - 1 \\ \\\implies \tt n - 1 = 34 \\ \\ \implies \tt n = 34 + 1 \\ \\ \implies \underline{\boxed{ \tt n = 35}}$

35 numbers lie between 50 and 250 which is multiple of 7

Answer 2

${\huge{\bf{\green{\mathfrak{\underline{\underline{Solution}}}}}}}$

Multiple of 7 between 50 and 250 are :

→ 7 , 14 , 21 ,......... , 245

By using A.P formula

\large\implies \boxed { \tt A_n = a + (n - 1)d}⟹

A

n

⠀⠀⠀⠀⠀⠀⠀⠀⠀ =a+(n−1)d

Here,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀a = 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀d = 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Aₙ = 245

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Substitute values in formula

\begin{gathered}\implies \tt245 = 7 + (n - 1)7 \\ \\ \implies \tt245 - 7 = (n - 1)7 \\ \\ \implies \tt238 = (n - 1)7 \\ \\ \implies \tt \frac{238}{7} = n - 1 \\ \\\implies \tt n - 1 = 34 \\ \\ \implies \tt n = 34 + 1 \\ \\ \implies \underline{\boxed{ \tt n = 35}}\end{gathered}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹245=7+(n−1)7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹245−7=(n−1)7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹238=(n−1)7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7/238

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀=n−1

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹n−1=34

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹n=34+1

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀n=35

35 numbers lie between 50 and 250 which are the multiples of 7.

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