Math homework again
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deborah0

05.03.2020

Mathematics

Multiples of 5 are 5, 10, 15, 20, etc.this is an arithmetic sequence with a common difference of 5.the sum of the terms in an arithmetic sequence is an an arithmetic series. the sum of an arithmetic series with $n$ terms is $s_n = \dfrac{n}{2}(a_1 + a_n)$ if we have the first term $a_1 = 5$ and the last term as $a_n = 105$ , with common difference $d = 5$ , then we can find the number of terms using the explicit rule. $\begin{aligned} a_n & = a_1 + d(n-1) \\ 105 & = 5 + 5(n-1) \\ 100 & = 5n - 5 \\ 105 & = 5n \\ n & = 21 \end{aligned}$ so using this with the sum formula, $\begin{aligned} s_n & = \dfrac{n}{2}(a_1 + a_n) \\ & = \dfrac{21}{2}(5 + 105) \\ & = 1155 \end{aligned}$ 1155

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