Question

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

Answer 1

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.

• $S_n = \frac{n}{2}(a+a_n)$

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

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

• $\implies S_{45}=45*135$

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