Arithmetic Sequences, in Depth
Read this topicExplanations 12
- An arithmetic sequence is a sequence where the difference between consecutive terms is the same. Good! For some terminology, the common difference of an arithmetic sequence is t…
By Ray Li, Victor Wang, Po-Shen Loh, Ruiran Xun
- Arithmetic sequences are sequences where, between each two consecutive terms, there is a common difference. For example, 1,2,3,4,5,6,7,...1,2,3,4,5,6,7,...1,2,3,4,5,6,7,... is a…
By Vincent Huang
- There is a simple way to find the nth term in an arithmetic sequence. First we should make sure that we are clear on what an arithmetic sequence is. An arithmetic sequence is ca…
By Tarang Saluja, Ruiran Xun
- There is a clever way to find the amount of terms in an arithmetic sequence. Let us go over what an arithmetic sequence is. It is a sequence with a common difference. So the ter…
By Tarang Saluja
- Arithmetic Sequences! An arithmetic sequence is a sequence in which there is a common difference between the terms. If the first term is aaa and the difference is ddd then the s…
By Tarang Saluja, Misha Lavrov, Po-Shen Loh, Ruiran Xun, Tong-Kiat Tan
- Recall that an arithmetic sequence is in the form xk=d(k−1)+x1x_k=d(k-1)+x_1xk=d(k−1)+x1, where ddd is the common difference, and x1x_1x1 is the first term. Ways an arithmeti…
By Farrell Eldrian Wu, Expii Team, Alex Federspiel, Joshua Siktar
- An arithmetic sequence is a sequence where each successive term differs by a constant amount. The arithmetic sequence resembles the sequence: an=an−1+da_n = a_{n-1} + dan=an−1…
By Winston Ou, Ruiran Xun
- An arithmetic sequence is a sequence where the difference between adjacent terms is constant. The differences between the terms in the sequence above are: 2,4,8,⋯2, 4, 8,\cdots2…
By Michael Yang, Ruiran Xun
- An arithmetic series (or sometimes called sequence) is the most basic of all kinds of series. Consider the following series. 4+7+10+11+…4+7+10+11+\ldots4+7+10+11+… If we ask our…
By Vivian Loh, amaterasu
- সমান্তর ধারা হচ্ছে এমন একটি ধারা যেখানে প্রতি ২ টি ক্রমিক সংখ্যার সাধারণ ব্যাবধান থাকবে। ভালো! কিছু পরিভাষার জন্য, সমান্তর ধারার বৈশিষ্ঠই হচ্ছে ক্রমিক পদের সাধারণ ব্যাবধান আপনি …
By Arko Roy, Zawadx · বাংলা
- সমান্তর ধারা সমান্তর ধারা হলো এমন একটি ধারা যেখানে সব সন্নিহিত পদের পার্থক্য সমান। যদি প্রথম পদটি হয় aaa আর পার্থক্য হয় ddd তাহলে ধারাটি হবে a+d,a+2d,a+3d⋯a+d,a+2d,a+3d \cdotsa+…
By Thamim Zahin · বাংলা
- (Video) Hard Arithmetic and Geometric Progression Questions by Eddie Woo Here's a video by Eddie Woo where he goes over some harder questions involving arithmetic progressions a…
By Alex Federspiel, Ruiran Xun, Caroline K
Problems 30
- An arithmetic sequence has first term 333 and common difference 222. What is the fifth term?
- An arithmetic sequence {ai}\{a_i\}{ai} satisfies a5=13a_5 = 13a5=13 and a11=105a_{11} = 105a11=105. What is a8a_8a8?
- Find the eighth term of the sequence 1440,1716,1848,…1440, 1716, 1848, \ldots1440,1716,1848,…, whose terms are formed by multiplying the corresponding terms of two arithmetic se…
- Which of the following are arithmetic sequences?
- What's the first term of an arithmetic sequence that has 404040 as the 101010th term and 555 as the constant difference?
- In how many ways can 345345345 be written as the sum of an increasing sequence of two or more consecutive positive integers? (2016 AMC 10B)
- What is the 50th50^{\text{th}}50th number in the following arithmetic sequence? 4,7,10,13,16,19,…4, 7, 10, 13, 16, 19, \dots4,7,10,13,16,19,…
- If the 4th4^{\text{th}}4th term of an arithmetic sequence is 666, and the 7th7^{\text{th}}7th term of the sequence is 888, find the 13th13^{\text{th}}13th term of the sequence.
- In the sequence of positive numbers 4,a,b,124, a, b, 124,a,b,12, the first three terms form a geometric progression and the final three terms form an arithmetic progression. Com…
- Say that an integer AAA is yummy if there exist several consecutive integers (including AAA) that add up to 201420142014. What is the smallest yummy integer? (Hint: AAA need not…
- Three distinct real numbers form (in some order) a 3-term arithmetic sequence, and also form (in possibly a different order) a 3-term geometric sequence. Compute the greatest po…
- এদের মধ্যে কোনগুলো সমান্তর ধারা?
বাংলা
- ১, ২১, ৪১, এই সমান্তর ধারার সাধারণ ব্যাবধান কী?
বাংলা
- ৭, ৫, ৩, ১, ... এই সমান্তর ধারার সাধারণ ব্যাবধান কী?
বাংলা
- ৫, ৫, ৫, ৫, ... এই সমান্তর ধারার সাধারণ ব্যাবধান কী?
বাংলা
- A display of cans on a grocery shelf consists of 161616 cans on the bottom, 141414 cans in the next row, 121212 cans in the next row, and so on, until the top row has 444 cans. …
- For a week, Jerry earns 222 more dollars than he did the previous day for his job. On the first day, he earned 707070. How much will he earn on day seven?
- Jennifer is training for cross country. For a month, she runs 505050 more miles than she did the previous day. If on the first day she runs 200200200 miles, how many miles does …
- One day, Erica passes a candy shop and decides to organize candy jars according to how much they hold. Erica organizes and moves the candy around so that each jar has 555 less c…
- Write the first five terms of a sequence that begins with 333 and has the rule “Add 444.”
- What is the fourth term of a sequence that has the rule “Multiply by 222” and has 555 as the second term?
- Find the rule in the following sequence: 1,2,4,8,16,⋯1, 2, 4, 8, 16, \cdots1,2,4,8,16,⋯
- Find the rule in the following sequence: 500,100,20,4,45,⋯500, 100, 20, 4, \frac{4}{5}, \cdots500,100,20,4,54,⋯
- What is the 333rd term of a sequence that begins with 222 has the rule “Add 777”?
- Once Erica finishes her job, she passes a pet shop and decides to organize cats according to how much they weigh. She moves the cats in the window around so that each cat weighs…
- The first term of an arithmetic sequence is 555 and the third term is 131313. What is the value of the 11th term?
- The common difference of a 121212-term arithmetic sequence is 111111. What is the difference between its 9th term and 3rd term?
- For positive integers nnn consider the sequence a1=1,a2=12,a3=1+32,a4=1+32+4,a5=1+3+52+4…a_1 = 1, a_2 = \frac{1}{2}, a_3 = \frac{1+3}{2}, a_4 = \frac{1+3}{2+4}, a_5 = \frac{1+3+…
- A display of cans on a grocery shelf consists of 161616 cans on the bottom, 141414 cans in the next row, 121212 cans in the next row, and so on, until the top row has 444 cans. …
- One day, Erica passes a candy shop and decides to organize candy jars according to how much they hold. Erica organizes and moves the candy around so that each jar has 555 less c…