Download Geometric Sequence and Series and more Exercises Mathematics in PDF only on Docsity!
Geometric
Sequence and Series
For educational purposes only
Mathematics for Grade 10 Science, Technology, and Engineering
III. Practice Exercises Show your complete solutions.
1. Determine the sum of the first 6 terms of the GS an = 5(4)n. Finding the first term: Finding r: an = 5(4)n^ an = a 1 rn- a 1 = 5(4)^1 a 2 = 20r2- a 1 = 5(4) 80 = 20r a 1 = 20 4 = r _ _ Finding the second term: Calculating for the sum: a 2 = 5(4)^2 Sn = ๐ 1 โ ๐ 1 ๐๐ 1 โ ๐ a 2 = 5(16) S 6 = 20 โ 20(4) 6 1โ a 2 = 80 S 6 = 20 โ 20(4096)โ S 6 = โ81900โ S 6 = 27300 The sum of the first six terms of the GS an = 5(4)n is 27,300.
2. Evaluate the infinite geometric series 6 + 30 + 150 + 170 + 750 + ... Finding r: Evaluating the infinite geometric series: an = a 1 rn-1^ S โ= ๐ 1 1โ๐ a 2 = 6r2-1^ S โ= (^) 1โ5^6 30 = 6r S โ= (^) โ4^6 5 = r S โ = (^) โ2^3
3. Determine the geometric mean between -6, and -50. GM = ๐๐ The geometric mean GM = (โ 6)(โ 50) between -6 and -50: GM = 300 ยฑ 17. 32 ๐๐ ยฑ 10 3 GM = ยฑ 17. 32 ๐๐ ยฑ 10 3
4. Insert two geometric means between -343, and 1. Looking for r: Looking for the means: an = a 1 rn-1^ a 2 = a 1 (r) = -343( โ 17 ) a 4 = -343(r)4-1^ a 2 = โ343 7 = - 1 = -343r^3 a 2 = - = r^3 a 3 = a 2 (r) = -49( ) 1 โ343 โ^ 1 7 = r a 3 = = - 3 1 โ โ 7 - 17 = r a 3 = -
ใ
ก
5. What is the 15th term of the sequence 4, -8, 16, -32, 64, โฆ? Finding r: Looking for the 15th term: an = a 1 rn-1^ an = a 1 rn- a 2 = 4r2-1^ a 15 = 4r15- -8 = 4r a 15 = 4(-2)^14 -2 = r a 15 = 4(16384) a 15 = 65536 ใ
ก 6. Write the nth term of the geometric sequence with a first term of 3 and a common ratio of 4. Finding the nth term: The nth term of the sequence: an = a 1 rn-1^ an = 3(4)n- an = 3(4)n- II.^ I. III. IV. Evaluation Encircle the letter of the correct answer. Use a separate pad paper for your solutions.
- Find the 5th term of a geometric sequence where the first term is 7 and the common ratio is 6. a. 1 512 b. 9 072 c. 5 072 d. 1 072
- If two geometric means are inserted between 6 and 162, find the second geometric mean. a. 12 b. 18 c. 54 d. 62
- What is the geometric mean between 120, and 30? a. 30 b. 40 c. 50 d. 60
- What is the nth term of the geometric sequence 3, 6, 12, 24, 28, 96, โฆ? a. an = 3 + 2(n - 1) b. an = 3(2)n- c. an = 2n + 1 d. an = 2(3)n-
- Find the sixth term of a geometric sequence where the second term is 6 and the common ratio is 2. a. 94 b. 95 c. 96 d. 97
- What is the common ratio in the geometric sequence 32, 16, 8, 4, 2, โฆ? a. 2 b. ยผ c. ยฝ d. 4
- If there are 500 bacteria at the end of the first day, how many will there be after 15 days if the bacteria double in number every day? a. 16 384 b. 8 192 000 c. 32 768 d. 16 384 000
- The common ratio of a geometric sequence is 3 and the sum of the first five terms is 968. Find the value of the first term. a. 6 b. 4 c. 8 d. 2
