Math  /  Algebra

Question1. Find the 11 th term of the geometric sequence. 17,17,17,-17,-17,-17, \ldots
3. Find the 10 th term of the geometric sequence. 17,34,68,17,34,68, \ldots
5. Find the 8 th term of the geometric sequence. 11,33,99,11,33,99, \ldots
7. Find the 12 th term of the geometric sequence. 16,32,64,-16,-32,-64, \ldots
2. Find the 11th term of the geometric sequence. 15,45,135,-15,45,-135, \ldots
4. Find the 8 th term of the geometric sequence. 1,2,4,-1,-2,-4, \ldots
6. Find the 8 th term of the geometric sequence. 1,2,4,1,-2,4, \ldots
8. Find the 7 th term of the geometric sequence. 10,20,40,-10,20,-40, \ldots

Studdy Solution

STEP 1

1. A geometric sequence has a constant ratio, denoted as rr, between consecutive terms.
2. The nn-th term of a geometric sequence can be found using the formula an=arn1a_n = a \cdot r^{n-1}, where aa is the first term and nn is the term number.

STEP 2

1. Find the 11th term of the geometric sequence 17,17,17,-17,-17,-17, \ldots.
2. Find the 10th term of the geometric sequence 17,34,68,17,34,68, \ldots.
3. Find the 8th term of the geometric sequence 11,33,99,11,33,99, \ldots.
4. Find the 12th term of the geometric sequence 16,32,64,-16,-32,-64, \ldots.
5. Find the 11th term of the geometric sequence 15,45,135,-15,45,-135, \ldots.
6. Find the 8th term of the geometric sequence 1,2,4,-1,-2,-4, \ldots.
7. Find the 8th term of the geometric sequence 1,2,4,1,-2,4, \ldots.
8. Find the 7th term of the geometric sequence 10,20,40,-10,20,-40, \ldots.

STEP 3

Identify the first term aa and the common ratio rr of the sequence 17,17,17,-17,-17,-17, \ldots.
a=17,r=1717=1 a = -17, \quad r = \frac{-17}{-17} = 1

STEP 4

Use the formula for the nn-th term to find the 11th term a11a_{11}.
a11=ar111=17110=17 a_{11} = a \cdot r^{11-1} = -17 \cdot 1^{10} = -17

STEP 5

Identify the first term aa and the common ratio rr of the sequence 17,34,68,17,34,68, \ldots.
a=17,r=3417=2 a = 17, \quad r = \frac{34}{17} = 2

STEP 6

Use the formula for the nn-th term to find the 10th term a10a_{10}.
a10=ar101=1729=17512=8704 a_{10} = a \cdot r^{10-1} = 17 \cdot 2^9 = 17 \cdot 512 = 8704

STEP 7

Identify the first term aa and the common ratio rr of the sequence 11,33,99,11,33,99, \ldots.
a=11,r=3311=3 a = 11, \quad r = \frac{33}{11} = 3

STEP 8

Use the formula for the nn-th term to find the 8th term a8a_8.
a8=ar81=1137=112187=24057 a_8 = a \cdot r^{8-1} = 11 \cdot 3^7 = 11 \cdot 2187 = 24057

STEP 9

Identify the first term aa and the common ratio rr of the sequence 16,32,64,-16,-32,-64, \ldots.
a=16,r=3216=2 a = -16, \quad r = \frac{-32}{-16} = 2

STEP 10

Use the formula for the nn-th term to find the 12th term a12a_{12}.
a12=ar121=16211=162048=32768 a_{12} = a \cdot r^{12-1} = -16 \cdot 2^{11} = -16 \cdot 2048 = -32768

STEP 11

Identify the first term aa and the common ratio rr of the sequence 15,45,135,-15,45,-135, \ldots.
a=15,r=4515=3 a = -15, \quad r = \frac{45}{-15} = -3

STEP 12

Use the formula for the nn-th term to find the 11th term a11a_{11}.
a11=ar111=15(3)10=1559049=885735 a_{11} = a \cdot r^{11-1} = -15 \cdot (-3)^{10} = -15 \cdot 59049 = -885735

STEP 13

Identify the first term aa and the common ratio rr of the sequence 1,2,4,-1,-2,-4, \ldots.
a=1,r=21=2 a = -1, \quad r = \frac{-2}{-1} = 2

STEP 14

Use the formula for the nn-th term to find the 8th term a8a_8.
a8=ar81=127=1128=128 a_8 = a \cdot r^{8-1} = -1 \cdot 2^7 = -1 \cdot 128 = -128

STEP 15

Identify the first term aa and the common ratio rr of the sequence 1,2,4,1,-2,4, \ldots.
a=1,r=21=2 a = 1, \quad r = \frac{-2}{1} = -2

STEP 16

Use the formula for the nn-th term to find the 8th term a8a_8.
a8=ar81=1(2)7=1(128)=128 a_8 = a \cdot r^{8-1} = 1 \cdot (-2)^7 = 1 \cdot (-128) = -128

STEP 17

Identify the first term aa and the common ratio rr of the sequence 10,20,40,-10,20,-40, \ldots.
a=10,r=2010=2 a = -10, \quad r = \frac{20}{-10} = -2

STEP 18

Use the formula for the nn-th term to find the 7th term a7a_7.
a7=ar71=10(2)6=1064=640 a_7 = a \cdot r^{7-1} = -10 \cdot (-2)^6 = -10 \cdot 64 = -640
_SOLUTION_:
1. The 11th term of the geometric sequence 17,17,17,-17,-17,-17, \ldots is 17-17.
2. The 10th term of the geometric sequence 17,34,68,17,34,68, \ldots is 87048704.
3. The 8th term of the geometric sequence 11,33,99,11,33,99, \ldots is 2405724057.
4. The 12th term of the geometric sequence 16,32,64,-16,-32,-64, \ldots is 32768-32768.
5. The 11th term of the geometric sequence 15,45,135,-15,45,-135, \ldots is 885735-885735.
6. The 8th term of the geometric sequence 1,2,4,-1,-2,-4, \ldots is 128-128.
7. The 8th term of the geometric sequence 1,2,4,1,-2,4, \ldots is 128-128.
8. The 7th term of the geometric sequence 10,20,40,-10,20,-40, \ldots is 640-640.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord