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
Alex Ar [27]
3 years ago
5

the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Mathematics
1 answer:
Nady [450]3 years ago
3 0

Given:

In an arithmetic sequence,

a_1=2

a_i=a_{i-1}-3

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

a_i=a_{i-1}+d         ...(i)

Where, d is the common difference.

We have,

a_i=a_{i-1}-3          ...(ii)

On comparing (i) and (ii), we get

d=-3

The sum of first i terms of an arithmetic sequence is:

S_i=\dfrac{i}{2}[2a+(i-1)d]

Putting i=335,a=2,d=-3, we get

S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]

S_{335}=\dfrac{335}{2}[4+(334)(-3)]

S_{335}=\dfrac{335}{2}[4-1002]

S_{335}=\dfrac{335}{2}(-998)

On further simplification, we get

S_{335}=335\times (-499)

S_{335}=-167165

Therefore, the sum of the first 335 terms in the given sequence is -167165.

You might be interested in
Below is the graph of y=b^x. Find b.
omeli [17]
Y = <span>b^x

when x = 1
y = b^1
y  = b

Therefore, the value of b is the same as the value of y when x =1
From the graph,
When x = 1, y = 0.5
Therefore, b = 0.5


To confirm this

From the graph,

When x = -1, y = 2
Since </span>y = b^x<span>
2 = </span>b^-1
2 = 1/b
2b = 1
b = 0.5

When x = -2, y = 4
Since y = b^x
4 = b^-2
4 = 1/(b^2)
b^2 = 1/4
b = √(1/4)
b = 1/2
b = 0.5

Therefore, it is conformed that b = 0.5

5 0
2 years ago
Read 2 more answers
Evaluate the question below<br> .<br> 12-2
MAXImum [283]

Answer:

=>12-2

=> 10

<em><u>You're Welcome</u></em>

<em><u>Hope this helps you.</u></em>

<h2><em><u>Pls</u></em><em><u>, mark it as the brainliest. I need it.</u></em></h2>
8 0
2 years ago
The function rule of a certain function is y = -3x + 1. If the input is 7, what is the output?
OleMash [197]

The output is -20 to this question

7 0
3 years ago
Explain how to determine if the number is a solution to the equation. n + 6 = 33 for n = 27
stepan [7]
If you subtract 6 from 33 youll end up with 27 and therefore 27 plus 6 equals 33
8 0
3 years ago
Read 2 more answers
Omar ordered his sister a birthday card from a company that randomly selects a card from their inventory. The company has 21 tot
Ksju [112]

Answer:

P = 7

Step-by-step explanation:

We have 21 total cards and out of those 21 cards, 14 of those are birthday cards. So that means that the amount of cards that are not birthday cards is the number of cards subtracted by the number of birthday cards, also shown as 21 - 14. So 21 - 14 = P, so now we solve what 21 - 14 is which is 7, so that means P = 7.

Let me know if you have any questions.

8 0
3 years ago
Other questions:
  • Owen surveyed his class on their favorite subject. The results are shown in the table. What is the relative frequency of someone
    7·2 answers
  • What is the answer to 3/2•5/4•7/3
    10·1 answer
  • Eric reflected parallelogram ABCD across the x-axis. If angle A is 125° and angle B is 55°, what is the degree measurement of an
    12·1 answer
  • Please tell me b. Do not want to think right now. Thanks.
    6·1 answer
  • Just some simple math fro points reward brainliest
    14·1 answer
  • If b^2=a then b is what of a?
    6·2 answers
  • If x = 6 units, y = 3 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
    8·1 answer
  • How do I pick what subject I'm trying to get an answer for<br>​
    5·2 answers
  • A store buys 8 sweaters for $72 and sells them for $288. How much profit does the store make per sweater?
    14·2 answers
  • What is the value of 6 in the number 7689​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!