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Brums [2.3K]
3 years ago
7

A recursion formula and the initial term of a sequence are given. Write out the first five terms of the sequence. a Subscript fo

nt size decreased by 1 1equals6​, a Subscript n plus font size decreased by 1 1equalsminusa Subscript n
Mathematics
1 answer:
Lelu [443]3 years ago
4 0

Answer:

6, -6, 6, -6 and 6.

Step-by-step explanation:

Given the recursion formula for a sequence

a_{n+1}=-a_n\\$where a_1=6\\

The first five terms of the sequence are:

\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6

Therefore, the first five terms of the sequence:

a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.

You might be interested in
A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?
Llana [10]

Answer:

The correct option is;

21 ft

Step-by-step explanation:

The equation of the parabolic arc is as follows;

y = a(x - h)² + k

Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)

We therefore have;

y = a(x - 20)² + 25

Whereby the parabola starts from the origin (0, 0), we have;

0 = a(0 - 20)² + 25

0 = 20²a + 25 → 0 = 400·a + 25

∴a = -25/400 = -1/16

The equation of the parabola is therefore;

y = (-\frac{1}{16})(x-20)^2 + 25

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28

Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;

y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft.

4 0
3 years ago
What is 20 time 4 equal?
IRISSAK [1]
20 multiplied (times) 4 is equal to 80 c:
3 0
3 years ago
Read 2 more answers
PLZ HELP!!!!
Vaselesa [24]
L=3$-x×2 x=D hope this helps?
3 0
3 years ago
Read 2 more answers
What is the answer to my problem
Nadya [2.5K]
Please provide more context for our brains to understand your problem (: thank you!
7 0
2 years ago
Please help !! Use Pythagorean theorem :) and show your work if you can thanks :”) will give b
g100num [7]

Answer:

b=\sqrt{1575} ≈ 39.7ft

Step-by-step explanation:

The Pythagorean theorem:

a^{2}+ b^{2}= c^{2}

(a and b are the two shorter legs and c is the largest leg, which is also the opposite side of the right angle)

First, the value of a and c is given. So, we can go ahead and plug those value in and then solve for b.

45^{2}+ b^{2}= 60^{2}

2025+b^{2} =3600

To find b, we have to get it by itself. So we subtract 2025 from both sides then square root both sides. Resulting in:

b^{2} =1575

b=\sqrt{1575} ≈ 39.7ft

7 0
3 years ago
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