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
Step-by-step explanation:
1.https://brainly.ph/question/756093
2.https://brainly.ph/question/1515916
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