Question

How many numbers between 70 and 5010 are divisible by 5

Answer 1

☯ GiveN :

• A.P : 75, 80, 85, 90 ........ 5005
• First term (a) = 75
• Common Difference (d) = 5
• Last term (An) = 5005

$\rule{200}{1}$

☯ To FinD :

We have to find the number of terms (n).

$\rule{200}{1}$

☯ SolutioN :

We know that,

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

★ Putting Values ★

$\sf{\dashrightarrow 5005 = 75 + (n - 1)5} \\ \\ \sf{\dashrightarrow 5005 = 75 + 5n - 5} \\ \\ \sf{\dashrightarrow 5005 = 70 + 5n} \\ \\ \sf{\dashrightarrow 5005 - 70 = 5n} \\ \\ \sf{\dashrightarrow 4935 = 5n} \\ \\ \sf{\dashrightarrow n = \frac{\cancel{4935}}{\cancel{5}}} \\ \\ \sf{\dashrightarrow n = 987} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n = 987}}}}}$

Answer 2

$\Large{\leadsto{\purple{\boxed{\boxed{\sf{A_n = a + (n - 1)d}}}}}}$

$\begin{lgathered}\sf{\dashrightarrow 5005 = 75 + (n - 1)5} \\ \\ \sf{\dashrightarrow 5005 = 75 + 5n - 5} \\ \\ \sf{\dashrightarrow 5005 = 70 + 5n} \\ \\ \sf{\dashrightarrow 5005 - 70 = 5n} \\ \\ \sf{\dashrightarrow 4935 = 5n} \\ \\ \sf{\dashrightarrow n = \frac{\cancel{4935}}{\cancel{5}}} \\ \\ \sf{\dashrightarrow n = 987} \\ \\ \Large{\mapsto{\orange{\boxed{\boxed{\sf{n = 987}}}}}}\end{lgathered}$