Find so that the numbers 2 +1, 3 + 4, 7 +6 form a geometric sequence.
Home
/
Find so that the numbers 2 +1, 3 + 4, 7 +6 form a geometric sequence
Find so that the numbers 2 +1, 3 + 4, 7 +6 form a geometric sequence.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
Solve the following problems.
1. What is the common ratio of the geometric sequence 2, -6, 18, ...?
2. Find the common ratio r of a geometric sequence in which the first is 5 and second term is 15.
3. Determine the common ratio r of an increasing geometric sequence, for which the first term is 5 and the third term is 20.
4. Find the common ratio r of an alternating geometric sequence an, for which a1 =125, a2= -25, and a1=5.
5. Find the fourth term of a geometric sequence, whose first term is 2 and the common ratio is 3.
6. Let an be a geometric sequence with common ratio r = 1/2. If a⁴=12, find a¹.
7. If a4 = 12, find a1. 7. Let an be an increasing geometric sequence. If the term a1 = 2 and the fifth term as = 162, determine a³.
8. Write down the 8th term in the geometric 1, 3, 9,... 9. Find the number of terms in the geometric sequence 6, 12, 24,...,1536.
10. What is the 6th term of the geometric sequence ? 11. Find the tenth term of a geometric sequence whose second term is 6 and the fourth term is 24?
12. What is the seventh term of a geometric sequence where the fourth term is 24 and the common ratio is 2? 13. Find k so that the terms k-3, k + 1, and 4k-2 form a geometric sequence. 14. The second term of a geometric sequence is and the fourth term is 15. Find the first term.
15. Find the 20th term of the geometric sequence whose third and seventh terms are -2 and - 32. respectively.
Answer:
e = -1 or e = 2
Step-by-step explanation:
Given: 2e + 1, 3e + 4, 7e + 6
Solution:
3e + 4 = 7e + 6
2e + 1 3e + 4
(7e + 6) (2e + 1) = (3e + 4) (3e + 4)
14e^2 + 7e + 12e + 6 = 9e^2 + 12e + 12e + 16
14e^2 + 19e + 6 = 9e^2 + 24e + 16
14e^2 - 9e^2 + 19e - 24e + 6 - 16 = 0
5e^2 - 5e - 10 = 0
(5e + 5) (e - 2) = 0
5e = -5 e = 2
-5 -5
e = -1
NOTE: Please check if I had any mistakes regarding the signs or construction of the equation. Hope it helps!