Sums of Geometric Sequences
Understanding the concept of sums of geometric sequences is fundamental in various mathematical applications. Geometric sequences, characterized by a common ratio between consecutive terms, offer a systematic way to model real-world phenomena such as population growth, interest accrual, and exponential decay. In this introductory paragraph, we will explore the principles behind sums of geometric sequences, including their formulas and properties, laying the groundwork for a deeper understanding of their significance in mathematics and beyond.
Questions
- What is the sum of a 7–term geometric series if the first term is –6, the last term is –24,576, and the common ratio is 4?
- A1=8, r=3 what are the first 12 terms?
- What is the sum of the first five terms of a geometric series with a1=10 and r=1/5?
- The positive numbers e and f are the 2nd and 14th terms respectively of an arithmetic progression whose first term is 1.It is also given that e,9 and f are three consecutive terms of a geometric progression. Find the values of e and f. ?
- If #a,a_1, a_2,.....a_10,b# are in A.P and #a,g_1,g_2,g_3................g_10,b# are in G.P and h is the H.M between a and b, then find the value of below given expression?
- How to find the common ratio of geometric sequence when the sum of 5th term to 8th term is twice the first four terms?
- How do you write a geometric series for which r=1/2 and n=4?
- In a geometric sequence , the common ratio and the second term are 2 and 30 respectively. find the value of a and the sum of the first eight terms ?
- What is the sum of a 6–term geometric series if the first term is 20 and the last term is 336,140?
- How do you find #S_n# for the geometric series #a_1=4#, r=0.5, n=8?
- If the third term is 3 of a geometric is 36 and the sixth term is 9/2, what is the explicit formula for the sequence ?
- Formulate the recursive formula for the following geometric sequence. {-16, 4, -1, ...} ?
- Find 5 geometric mean between 1 and 27?
- What is the tenth term of the geometric sequence with #a_1 =4# and #r = 1/2#?
- What is the sum of the first 35 terms in the geometric series #8-12+18...#?
- How do you find the sum of the first 20 terms of the sequence 1, -3, 9,...?
- Find the nth term An of the geometric sequence described below where r is the common ratio. Kind of confused on what to do?
- Solving using geometric Series, #sqrt(2)/2, 1/2, 2^(3/2)/8,1/4#?
- Find the sum of the first n terms of the series : #1 + 2(1+1/n) + 3(1+1/n)^2 + 4(1+1/n)^3.......#?
- What is the sum of the geometric sequence 8, 16, 32?