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Gre4nikov [31]
3 years ago
9

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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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}}}}}
6 0
2 years ago
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