Question

find the sum of numers between 3 to 30 which are divisible by 3​

Answer 1

Answer:

3,6,9,12,15,16,18,21,24,27,30 done

Answer 2

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

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$\tt given\begin{cases} \sf{A.P : 6, 9, 12 .......27} \\ \sf{First \: term \: (a) = 6} \\ \sf{Common \: Difference \: (d) = 3} \\ \\ \sf{Last \: term \: (An)}\end{cases}$

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

We have to find their sum.

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

We know that,

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

$\sf{\mapsto 27 = 6 + (n - 1)3} \\ \\ \sf{\mapsto 27 - 6 = (n - 1)3} \\ \\ \sf{\mapsto 21 = (n - 1)3} \\ \\ \sf{\mapsto \frac{\cancel{21}}{\cancel{3}} = n - 1} \\ \\ \sf{n = 8}$

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Now,

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

$\sf{\mapsto S_n = \frac{\cancel{8}}{\cancel{2}} (6 + 27)} \\ \\ \sf{\mapsto S_n = 4 \times 33} \\ \\ \sf{\mapsto S_n = 132}$

$\Large{\boxed{\sf{S_n = 132}}}$

$\sf{\therefore \: Sum \: is \: 132}$