1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
storchak [24]
3 years ago
14

What is the sum of the first 37 terms of the arithmetic sequence?

Mathematics
1 answer:
lidiya [134]3 years ago
6 0

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

a_{n+1} = a_{n} + d

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

a_{n} = a_{1} + (n-1)*d

The sum of the first n terms of an arithmetic sequence is given by:

S_{n} = \frac{n(a_{1} + a_{n})}{2}

In this question:

a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6

We want the sum of the first 37 terms, so we have to find a_{37}

a_{n} = a_{1} + (n-1)*d

a_{37} = a_{1} + (36)*d

a_{37} = -27 + 36*6

a_{37} = 189

Then

S_{37} = \frac{37(-27 + 189)}{2} = 2997

The sum of the first 37 terms of the arithmetic sequence is 2997.

You might be interested in
Given scalene triangle DEF, explain how to find locus of points equidistant from DE EF DF using incenter
exis [7]
Points equidistant from DE EF are in the bisector of angle DEF
points equidistant from EF DF are in the bisector of angle EFD
the sought after point is the intersection of bisectricess of triangle




5 0
3 years ago
Calculate 32 percent of 133
Rasek [7]
0.32 x 133
=42.56
:) hope that helps
3 0
3 years ago
Read 2 more answers
Suppose you invest $50 a month in an annuity that earns 4% APR compounded monthly. How much money will you have in this account
skelet666 [1.2K]
To solve this we are going to use formula for the future value of an ordinary annuity: FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]
where
FV is the future value
P is the periodic payment
r is the interest rate in decimal form
n is the number of times the interest is compounded per year
t is the number of years

We know from our problem that the periodic payment is $50 and the number of years is 3, so P=50 and t=3. To convert the interest rate to decimal form, we are going to divide the rate by 100%
r= \frac{4}{100}
r=0.04
Since the interest is compounded monthly, it is compounded 12 times per year; therefore, n=12.
Lets replace the values in our formula:
FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]
FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]
FV=1909.08

We can conclude that after 3 years you will have $1909.08 in your account.
4 0
3 years ago
Read 2 more answers
Write the decimal 1,072.039 in words
Rina8888 [55]
One thousand seventy two point thirty nine thousandths.

3 0
3 years ago
Solve for X: -22=-7+3/5x
stira [4]



solution for the problem-

X=-22
3 0
3 years ago
Other questions:
  • If 3cot^2x - 5cotx = -2, then cotx = _____.
    8·1 answer
  • What is the mathematical expression for “the $100 earned was split between all the people and each got $12.50”?
    12·2 answers
  • How do you find the apothem of a pentagonal pyramid?
    13·1 answer
  • What is the percent of 50 is 80
    10·2 answers
  • The line plot shows the number of eggs found in each nest in a park. How many more nests had four eggs than two eggs?
    11·2 answers
  • The furniture store sells each chair (c) for $225. To have them shipped to their house, the store charges $60. If the Browns bou
    11·1 answer
  • A student pulls out ten marbles: three were red, two were blue, and five were green. In the next handful, the
    6·1 answer
  • What are some solutions to the inequality x>6?
    14·1 answer
  • You can buy 5 oranges for $2.50. What is the unit rate for 1 orange? How much would 8 oranges cost?
    10·1 answer
  • R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!