A f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
Answer/Step-by-step explanation:
Given:
m<MNQ = 132°
m<Q = 54°
m<P = 3x
1. m<MNQ = m<P + m<Q
Reason: exterior angle theorem of a triangle
Plug in the values
2. 132° = 3x + 54°
Reason: Substitution
3. x = 26
Reason: Algebra
132 - 54 = 3x (substraction property of equality)
78 = 3x
78/3 = x (division property of equality)
26 = x
x = 26
Answer:
soupp B
Step-by-step explanation:
Answer:
A). 101 inches
B). 110 years
Step-by-step explanation:
Years since planting Circumference Difference
1 3 -
2 5 (5 - 3) = 2
3 7 (7 - 5) = 2
4 9 (9 - 7) = 2
5 11 (11 - 9) = 2
6 13 (13 - 11) = 2
There is a difference of 2 in every successive term of the circumference.
Therefore, the given sequence is an arithmetic sequence.
Explicit formula of an arithmetic sequence is given by,
Here a = first term
n = number of terms
d = common difference
From the given table,
Here = circumference after 'n' years
n = Age of the plant
By this formula,
Circumference of a tree after 50 years,
= 101 inches
Age of tree with the circumference = 221 inches,
221 = 2n + 1
2n = 220
n = 110 years