Solving a Sequence Problem Homework Statement

  • Thread starter erisedk
  • Start date
  • Tags
    Sequence
In summary, the Homework statement asks for a solution to equations where the first n terms are consecutive. The Attempt at a Solution provides an equation for the sum of the first n terms, but says that the equation does not work if n is not a multiple of 6.
  • #1
erisedk
374
7

Homework Statement


Consider the sequence in the form of groups (1), (2,2), (3,3,3), (4,4,4,4), (5,5,5,5,5),...

i. The 2000th term of the sequence is not divisible by
(A) 3 (B) 9 (C) 7 (D) None of these

ii. The sum of the first 2000 terms is
(A) 84336 (B) 96324 (C) 78466 (D)None of these

iii. The sum of the remaining terms in the group after 2000th term in which 2000th term lies is
(A) 1088 (B) 1008 (C) 1040 (D) None of these

Homework Equations

The Attempt at a Solution


I don't know where to start!
For ii, I need to find 1^2 + 2^2 + 3^2 + 4^2... for which I have the formula n(n+1)(2n+1)/6, but I don't know what the preceding number of the group in which the 2000th term lies will be, so I can't even approximate an answer.
Just please tell me how to begin!
 
Physics news on Phys.org
  • #2
I need a bit more background. In what sense is (5,5,5,5,5) a group, and in what sense might it be divisible by an integer?
 
  • #3
1-first term 2-second term 2-third term 3-fourth term 3-fifth term 3-sixth term 4- seventh term
If the questions were-
The sixth term of the sequence is not divisible by-
(A)1 (B)2 (C)3
Then the answer would be (B) as 3 is not divisible by 2.

Sum of the first six terms-
Ans: 14

The sum of the remaining terms in the group after 6th term in which 6th term lies is
Ans: 0
OR
The sum of the remaining terms in the group after 5th term in which 5th term lies is
Ans: 3
 
  • #4
Sorry for the repeat post.

Moderator note: It's now deleted.
 
Last edited by a moderator:
  • #5
Ok, I see.
Not sure why you think you want the formula for the sum of consecutive squares. You are not trying to sum the series.
How many terms are there before the occurrence of the first n?
 
  • #6
Before the occurrence of the first n??
 
  • #7
erisedk said:
Before the occurrence of the first n??
As in, zero before the first 1, one before the first 2, three before the first 3, six before the first 4,... How many before the first n?
 
  • #8
n(n-1)/2 before the first n. What now?
 
  • #9
erisedk said:
n(n-1)/2 before the first n. What now?
So if the 2000th term is n, what equation can you write down?
 
  • #10
n(n-1)/2 < = 2000 ?
 
  • #11
Oh ok! n=63 gives 1953 numbers before 63. I got all the answers! Thank you so much :D
 

FAQ: Solving a Sequence Problem Homework Statement

How do I solve a sequence problem?

To solve a sequence problem, you need to first identify the type of sequence you are working with, such as arithmetic or geometric. Then, you can use a formula or pattern to find the next term in the sequence. It is also helpful to create a table or draw a diagram to visualize the sequence.

What are some strategies for solving sequence problems?

Some strategies for solving sequence problems include finding the difference or ratio between terms, using algebraic equations to represent the sequence, and looking for patterns or relationships between terms. It is also important to check your answer by plugging it back into the sequence.

What is the difference between an arithmetic and geometric sequence?

An arithmetic sequence has a common difference between each term, while a geometric sequence has a common ratio between each term. In an arithmetic sequence, each term is found by adding or subtracting a constant number to the previous term. In a geometric sequence, each term is found by multiplying or dividing by a constant number to the previous term.

How do I find the nth term in a sequence?

To find the nth term in a sequence, you can use a formula specific to the type of sequence you are working with. For example, in an arithmetic sequence, the formula is n = a + (n-1)d, where n is the term number, a is the first term, and d is the common difference. In a geometric sequence, the formula is an = a1(r)^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.

What are some real-life applications of sequence problems?

Sequence problems can be found in many real-life situations, such as financial planning, population growth, and patterns in nature. They can also be used in various fields of science, such as genetics, physics, and chemistry. Being able to identify and solve sequence problems is a valuable skill in many different industries.

Similar threads

How to Solve Arithmetic Sequence Problems
Replies
1
Views
1K
Straight line intersects geometric sequence
Replies
5
Views
1K
Find bounding numbers for two interrelated sequences
Replies
6
Views
2K
Find the two values of the common ratio- Geometric sequence
Replies
6
Views
1K
Geometric Sequence to solve an Interest Problem
Replies
2
Views
1K
Arithmetic Sequence Homework: Find the Sum
Replies
4
Views
2K
Finding Limit: Homework Statement & Solution
Replies
10
Views
2K
Values of x for which a geometric series converges
Replies
1
Views
4K
Arithmetic and Geometric sequence problem
Replies
4
Views
2K
Answer to Sequence Problem: Eighth Term
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top