Answer:
Finding the nth Term of a Sequence
In finding the nth term of any sequence, we need to know the common difference or ratio. To know the common difference or ratio, subtract or divide any two consecutive terms of the sequence. The common difference or ratio is used to find the next terms of the sequence. Be careful in addition especially if the common difference or ratio is a negative number.
Answers:
A. 30, 35, 40 Rule: add 5
B. 4, 0, -4 Rule: subtract 4
C. 11, 13, 15 Rule: add 2
D. -8, -10, -12 Rule: subtract 2
E. \frac{16}{28}
28
16
, \frac{25}{28}
28
25
, \frac{36}{28}
28
36
Rule: square the numerator, copy the denominator
F. 4, 0 , -4 Rule: subtract 4
G. 14, 17, 20 Rule: add 3
H. \frac{13}{7}
7
13
, \frac{15}{7}
7
15
, \frac{17}{7}
7
17
Rule: add \frac{2}{7}
7
2
I. 81, 243, 729 Rule: raise 3 to the nth power.
J. 30, 36, 42 Rule: add 6
Solutions:
A. 10, 15, 20, 25, ___, ___, ____
Given:
a₁ = 10
a₂ = 15
Find d.
d = a₂ - a₁
d = 15 - 10
d = 5
Find a₅.
a₅ = a₄ + d
a₅ = 25 + 5
a₅ = 30
Find a₆.
a₆ = a₅ + d
a₆ = 30 + 5
a₆ = 35
Find a₇.
a₇ = a₆ + d
a₇ = 35 + 5
a₇ = 40
Therefore, the next three terms are 30, 35, 40.
Rule: add 5
B. 20, 16, 12, 8, ___, ___, ___
Given:
a₁ = 20
a₂ = 16
Find d.
d = a₂ - a₁
d = 16 - 20
d = -4
Find a₅.
a₅ = a₄ + d
a₅ = 8 - 4
a₅ = 4
Find a₆.
a₆ = a₅ + d
a₆ = 4 - 4
a₆ = 0
Find a₇.
a₇ = a₆ + d
a₇ = 0 - 4
a₇ = -4
Therefore, the next three terms are 4, 0, - 4.
Rule: subtract 4
C. 5, 7, 9, ___, ___, ___
Given:
a₁ = 5
a₂ = 7
Find d.
d = a₂ - a₁
d = 7 - 5
d = 2
Find a₄.
a₄ = a₃ + d
a₄ = 9 + 2
a₄ = 11
Find a₅.
a₅ = a₄ + 2
a₅ = 11 + 2
a₅ = 13
Find a₆.
a₆ = a₅ + 2
a₆ = 13 + 2
a₆ = 15
Therefore, the next three terms are 11, 13, 15.
Rule: add 2
D. -2, -4, -6, ___, ___, ___
Given:
a₁ = -2
a₂ = -4
Find d.
d = a₂ - a₁
d = -4 - (-2)
d = -4 + 2
d = -2
Find a₄.
a₄ = a₃ - 2
a₄ = -6 - 2
a₄ = -8
Find a₅.
a₅ = a₄ - 2
a₅ = -8 - 2
a₅ = -10
Find a₆.
a₆ = a₅ - 2
a₆ = -10 - 2
a₆ = -12
Therefore, the next three terms of the sequence are -8, -10, -12.
Rule: subtract 2
E. \frac{1}{28}
28
1
, \frac{4}{28}
28
4
, \frac{9}{28}
28
9
, ___, ___, ___
Given:
a₁ = \frac{1}{28}
28
1
, n = 1
a₂ = \frac{4}{28}
28
4
, n = 2
Find r.
r = \frac{n^2}{28}
28
n
2
Find a₄.
a₄ = \frac{4^2}{28}
28
4
2
a₄ = \frac{16}{28}
28
16
Find a₅.
a₅ = \frac{5^2}{28}
28
5
2
a₅ = \frac{25}{28}
28
25
Find a₆.
a₆ = \frac{6^2}{28}
28
6
2
a₆ = \frac{36}{28}
28
36
Therefore, the next three terms of the sequence are \frac{16}{28}
28
16
, \frac{25}{28}
28
25
, \frac{36}{28}
28
36
.
Rule: square the numerator and copy the denominator
F. 20, 16, 12, 8, ___, ___, ___
Given:
a₁ = 20
a₂ = 16
Find d.
d = a₂ - a₁
d = 16 - 20
d = -4
Find a₅.
a₅ = a₄ - 4
a₅ = 8 - 4
a₅ = 4
Find a₆.
a₆ = a₅ - 4
a₆ = 4 - 4
a₆ = 0
Find a₇.
a₇ = a₆ - 4
a₇ = 0 - 4
a₇ = -4
Therefore, the next three terms of the sequence are 4, 0 , -4.
Rule: subtract 4
G. 2, 5, 8, 11, ___, ___, ___
Given:
a₁ = 5
a₂ = 2
Find d.
d = a₂ - a₁
d = 5 - 2
d = 3
Find a₅.
a₅ = a₄ + d
a₅ = a₄ + 3
a₅ = 11 + 3
a₅ = 14
Find a₆.
a₆ = a₅ + d
a₆ = 14 + 3
a₆ = 17
Find a₇.
a₇ = a₆ + d
a₇ = 17 + 3
a₇ = 20
Therefore, the next three terms of the sequence are, 14, 17, 20.
Rule: add 3
H. \frac{7}{7}
7
7
, \frac{9}{7}
7
9
, \frac{11}{7}
7
11
, ___, ___, ___
Given:
a₁ = \frac{7}{7}
7
7
a₂ = \frac{9}{7}
7
9
Find d.
d = a₂ - a₁
d = \frac{9}{7}
7
9
- \frac{7}{7}
7
7
d = \frac{2}{7}
7
2
Find a₄.
a₄ = a₃ + d
a₄ = \frac{11}{7}
7
11
+ \frac{2}{7}
7
2
a₄ = \frac{13}{7}
7
13
Find a₅.
a₅ = a₄ + d
a₅ = \frac{13}{7}
7
13
+ \frac{2}{7}
7
2
a₅ = \frac{15}{7}
7
15
Find a₆.
a₆ = a₅ + d
a₆ = \frac{15}{7}
7
15
+ \frac{2}{7}
7
2
a₆ = \frac{17}{7}
7
17
Therefore, the next three terms of the sequence are \frac{13}{7}
7
13
, \frac{15}{7}
7
15
, \frac{17}{7}
7
17
.
Rule: add \frac{2}{7}
7
2
I. 3, 9, 27, ___, ___, ___
Given:
a₁ = 3 = 3¹
a₂ = 9 = 3²
Find a₄.
a₄ = 3⁴
a₄ = 81
Find a₅.
a₅ = 3⁵
a₅ = 243
Find a₆.
a₆ = 3⁶
a₆ = 729
Therefore, the next three terms of the sequence are 81, 243, 729.
Rule: raise 3 to the nth power.
J. 6, 12, 18, 24, ___, ___, ___
Given:
a₁ = 6
a₂ = 12
Find d.
d = a₂ - a₁
d = 12 - 6
d = 6
Find a₅.
a₅ = a₄ + d
a₅ = 24 + 6
a₅ = 30
Find a₆.
a₆ = a₅ + d
a₆ = 30 + 6
a₆ = 36
Find a₇.
a₇ = a₆ + d
a₇ + 36 + 6
a₇ = 42
Therefore, the next three terms of the sequence are 30, 36, 42.
Rule: add 6
What is an arithmetic sequence:
https://brainly.ph/question/756093
How to find the nth term of an arithmetic sequence: https://brainly.ph/question/1515916
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Step-by-step explanation:
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