Question

5,10,15,20...... find at50​

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

$\rule{200}{1}$

★ Given :

• A.P : 5, 10, 15, 20 .......... 50
• First term (a) = 5
• Common Difference (d) = 5
• Last term ($\sf{A_n)}$ = 50

$\rule{200}{1}$

★ To Find :

We have to find the sum of all the terms.

$\rule{200}{1}$

★ Solution :

We know that,

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

$\sf{→ 50 = 5 + (n - 1)5} \\ \\ \sf{→ 50 = 5 + 5n - 5} \\ \\ \sf{→ 5n = 50}\\ \\ \sf{→ n = \frac{\cancel{50}}{\cancel{5}}} \\ \\ \sf{→ n = 10}$

$\rule{200}{2}$

Now,

$\Large{\implies{\boxed{\boxed{\sf{S_n = \frac{n}{2} (a + L)}}}}}$

$\sf{→ S_n = \frac{\cancel{10}}{\cancel{2}}(5 + 50)} \\ \\ \sf{→ S_n = 5(55)} \\ \\ \sf{→ S_n = 275}$