All categories

3 years ago

The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series?

Mathematics

2 answers:

JulsSmile [24]3 years ago

8 0

Answer:

b. 390

Step-by-step explanation:

$a_1 =3\\a_n=75\\n=10\\\\use \ the \ arithmetic\ formula \\\\S_n=\frac{n}{2}(a_1+a_n)\\S_1_0=\frac{10}{2} (3+75)\\\\ \\S_1_0= 5 (78)\\\\S_1_0=390\\$

USPshnik [31]3 years ago

3 0

The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1 + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390

You might be interested in

Find the length of the missing ride. ROUND YOUR ANSWER TO THE NEAREST TENTH

irakobra [83]

Using pythagorean theorem:

$\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{19^2-17^2} \\ b=\sqrt[]{72} \\ b\approx8.5 \end{gathered}$

8 0

1 year ago

dele took 25 minutes to walk to school and he arrived at exactly 8:00am, at what time did he leave his home

Roman55 [17]

I think it would be around 7:30am

4 0

3 years ago

Who wakes up early if so what time? what is 10^6 AND 60^10?

meriva

Answer:

I wake up around 7:00

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to h

Diano4ka-milaya [45]

Answer:

The total change in water level over the past 2 years is $\displaystyle -4 \frac{1}{6}$ .

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Fractions

Proper and Improper

Numbers

Least Common Multiple (LCM)

Step-by-step explanation:

Step 1: Define

Identify

Year 1 water change: $\displaystyle -2 \frac{1}{3}$

Year 2 water change: $\displaystyle -1 \frac{5}{6}$

Step 2: Find Total Water Change

[Set up] Add yearly water changes: $\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}$
[Fractions] Convert to improper: $\displaystyle \frac{-7}{3} - \frac{11}{6}$
[Fraction] Rewrite [LCM]: $\displaystyle \frac{-14}{6} - \frac{11}{6}$
[Order of Operations] Subtract: $\displaystyle \frac{-25}{6}$
[Fraction] Convert to proper: $\displaystyle -4 \frac{1}{6}$