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3 years ago

Are the figures below similar? Explain.

Mathematics

1 answer:

CaHeK987 [17]3 years ago

3 0

Answer:C
Explain: Just think so

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3 years ago

Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.

scoray [572]

Answer:

6075

Step-by-step explanation:

Given series is: 25 + 30 + 35 + ⋯ + 245.

Here, first term (a) = 25
Common difference (d) = 5
Last term $(a_n) = 245$

First we find the number of terms that this series has by the following formula:

$a_n = a+(n-1)d$

Plugging the values of a, d and $a_n$ , we find.

$245 = 25+(n-1)5$

$\implies 245 - 25=(n-1)5$

$\implies 220=(n-1)5$

$\implies \frac{220}{5}=n-1$

$\implies 44=n-1$

$\implies 44+1=n$

$\implies\red{\bold{ n=45}}$

Thus, the given series contains 45 terms.

Next, we find the sum of the given series using the formula given below.

$S_n = \frac{n}{2}(a+a_n)$

$\implies S_{45}= \frac{45}{2}(25+245)$

$\implies S_{45}= \frac{45}{2}(270)$

$\implies S_{45}=45*135$

$\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}$

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2 years ago