Question

5 + 10 + 15 +. . . . + 100 How much?

Answer 1

Answer:1050

pls refer my attachment:

Answer 2

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

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$\tt given\begin{cases} \sf{A.P : 5, 10, 15 ....... 100} \\ \sf{First \: term (a) = 5} \\ \sf{Common \: Difference (d) = 5} \\ \sf{Last \: term (L) = 100}\end{cases}$

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$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the sum of all the terms

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

Firstly, we will find the number of terms.

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

$\sf{→100 = 5 + (n - 1)5} \\ \\ \sf{→100 = \cancel{5} + 5n \cancel{-5}}\\ \\ \sf{→n = \frac{\cancel{100}}{\cancel{5}}} \\ \\ \sf{→n = 20}$

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Now,

We know that,

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

$\sf{→S_n = \frac{\cancel{20}}{\cancel{2}} (5 + 100)} \\ \\ \sf{→S_n = 10(105)} \\ \\ \sf{→S_n = 1050}$