Set whose terms are obtained by multiplying the preceding term by the same constant. Constant is known as the common ratio. Reciprocals also forms a geometric sequence since it has a common ratio. Common ration can be obtained by dividing the next term by the preceding term. Common ratio must not be equal to zero.
Answers:
Common Ratio Next 3 terms
2 32, 64, 128
36, 12. 4
-4 192, -568, 2272
5 12.5, 62.5, 312.5
10, 1,
Solutions:
1. 4, 8, 16, __, __, __
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
8 = 4r² ⁻ ¹
8 = 4r¹
8 = 4r
=
2 = r
Find the next 3 terms.
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
2. 972, 324, 108, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
324 = 972r²⁻¹
324 = 972r
=
= r
Find the next 3 terms.
108 × = = 36
36 × = = 12
12 × = = 4
3. -3, 12, -48, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
12 = -3r²⁻¹
12 = -3r¹
12 = -3r
=
-4 =r
Find the next 3 terms.
-48 x -4 = 192
192 x -4 = -568
-568 x -4 = 2272
4. 0.1, 0.5, 2.5, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
0.5 = 0.1r²⁻¹
0.5 = 0.1r
=
5 = r
Find the next 3 terms.
2.5 x 5 = 12.5
12.5 x 5 = 62.5
62.5 x 5 = 312.5
5. 10,000, 1,000, 100, ___, ____, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
Answers & Comments
Verified answer
Geometric Sequence
Set whose terms are obtained by multiplying the preceding term by the same constant. Constant is known as the common ratio. Reciprocals also forms a geometric sequence since it has a common ratio. Common ration can be obtained by dividing the next term by the preceding term. Common ratio must not be equal to zero.
Answers:
Common Ratio Next 3 terms
2 32, 64, 128
36, 12. 4
-4 192, -568, 2272
5 12.5, 62.5, 312.5
10, 1,
Solutions:
1. 4, 8, 16, __, __, __
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
8 = 4r² ⁻ ¹
8 = 4r¹
8 = 4r
=
2 = r
Find the next 3 terms.
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
2. 972, 324, 108, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
324 = 972r²⁻¹
324 = 972r
=
= r
Find the next 3 terms.
108 × = = 36
36 × = = 12
12 × = = 4
3. -3, 12, -48, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
12 = -3r²⁻¹
12 = -3r¹
12 = -3r
=
-4 =r
Find the next 3 terms.
-48 x -4 = 192
192 x -4 = -568
-568 x -4 = 2272
4. 0.1, 0.5, 2.5, ___, ___, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
0.5 = 0.1r²⁻¹
0.5 = 0.1r
=
5 = r
Find the next 3 terms.
2.5 x 5 = 12.5
12.5 x 5 = 62.5
62.5 x 5 = 312.5
5. 10,000, 1,000, 100, ___, ____, ___
Find the common ratio using the formula a_n = arⁿ ⁻ 1.
a_n = arⁿ ⁻ ¹
1,000 = 10,000r²⁻¹
1,000 = 10,000r
=
= r
Find the next 3 terms.
100 x = = 10
10 x = = 1
1 x =
What is a geometric sequence and examples: brainly.ph/question/4922152
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