Geometric Sequences, in Depth
Read this topicExplanations 5
- Let's see if we can find the formula for finding the nth term in a geometric sequence. Let's take a look at a pretty basic sequence first: 2,4,8,16,…2,4,8,16,\dots2,4,8,16,… It'…
By Pranav Sriram, Anish Sevekari, Ruiran Xun
- Geometric Sequences Intuitively, a geometric sequence is a sequence where a term in the sequence is found by multiplying the previous term by some constant number. More formally…
By Justin Biggs, Moor Xu, Ruiran Xun, Dani
- Try this! The first, third, and fourth terms of an increasing geometric sequence form an arithmetic progression. What is the common ratio of the sequence? Let the first term be …
By Vinjai Vale
- A geometric series or geometric progression is a series in which the ratio of any two consecutive terms is the same. This ratio is called the common ratio of the geometric progr…
By Rishin Aggarwal, Moor Xu, Ruiran Xun
- (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 8
- An elephant writes a sequence of numbers on a board starting with 111. Each minute, it doubles the sum of all the numbers on the board so far and, without erasing anything, writ…
- Two infinite geometric sequences both begin with 111. Their sums are reciprocals of each other. The common ratio of one of the sequences is 13\frac{1}{3}31. If the sum of the t…
- A test you are taking has twenty-four multiple choice questions, each with answers AAA, BBB, CCC, and DDD. How many possible solution sets are there for this test?
- Suppose that the second term of a geometric sequence is 333 and the fourth term is 272727. List all possible values for the first 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…
- If the first three terms of a geometric sequence are 3,31/3,31/6\sqrt3, 3^{1/3}, 3^{1/6}3,31/3,31/6, what is the fourth term?
- 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…
- If rar_ara is the common ratio of the first sequence and rbr_brb the common ratio of the second, what is the value of rarb\frac{r_a}{r_b}rbra?