MATHEMATICS HIGH SCHOOL

Given the arithmetic sequence, find the recursive formula, explicit formula, and the indicated term.8) 1,4,1, 10, ...
7) 12, 7, 2, -3,...

Answers

Answer 1
Answer:

Answer:

Let's find the recursive formula, explicit formula, and the indicated term for the given arithmetic sequences.

Sequence 1: 1, 4, 1, 10, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term alternates between adding 3 and subtracting 3.

Recursive formula:

a1 = 1 (the first term)

an = an-1 + (-1)^(n+1) * 3

For example, to find the 4th term (a4) using the recursive formula:

a1 = 1 (the first term)

a2 = a1 + (-1)^(2+1) * 3 = 1 + (-1) * 3 = -2

a3 = a2 + (-1)^(3+1) * 3 = -2 + 1 * 3 = 1

a4 = a3 + (-1)^(4+1) * 3 = 1 + (-1) * 3 = -2

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, since the terms alternate between adding 3 and subtracting 3, the common difference is not constant.

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

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Sequence 2: 12, 7, 2, -3, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term decreases by 5.

Recursive formula:

a1 = 12 (the first term)

an = an-1 - 5

For example, to find the 4th term (a4) using the recursive formula:

a1 = 12 (the first term)

a2 = a1 - 5 = 12 - 5 = 7

a3 = a2 - 5 = 7 - 5 = 2

a4 = a3 - 5 = 2 - 5 = -3

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, the common difference is -5.

Explicit formula:

an = 12 + (n - 1)(-5)

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

Please provide the term number or the position of the term in the sequence so that I can help you find the indicated term.

Step-by-step explanation:

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The first term of an AP is 5, common difference is 3 and the last term is 80. Find the number of terms.

Answers

Answer:

n=26

Step-by-step explanation:

an=a+(n-1)d

80=5+(n-1)3

80=5+3n-3

80-2=3n

78/3=n

n=26

Today the coast of a gallon of gas is $2.65. Every week for the next 10 weeks, it will increase by $0.05.a gallon. If you wrote a linear equation to model this situation,what would the slope be?

Answers

We don't need to know how many weeks it kept up
that same rate of increase.

You just told us that it increases by $0.05 a gallon each week.

So the slope of a graph during that period is  $0.05 / week.

Solve the following equations.X^2 + 5x + 6 = 0
(Factorise)

X^2 + 7x + 11 = 0
(Use the quadratic formula)

Answers

facotr
ax^2+bx+c=0
find what 2 number multiply to c and add to b
what 2 numbers multiply to 6 and add to 5
2 and 3
(x+2)(x+3)=0
set to zero
x+2=0
x=-2
x+3=0
x=-3
x=-2 or -3



other one
for ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}

we are given
x^2+7x+11=0
a=1
b=7
c=11

sub
x=\frac{-7+/- \sqrt{7^(2)-4(1)(11)} }{2(1)}
x=(-7+/- √(49-44) )/(2)
x=(-7+/- √(5) )/(2)
x=(-7+ √(5) )/(2) or (-7- √(5) )/(2)

What is the derivative of x cubed?

Answers

Answer:

\displaystyle (dy)/(dx)[x^3] = 3x^2

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

\displaystyle y = x^3

Step 2: Differentiate

  1. Basic Power Rule:                                                                                            \displaystyle y' = 3x^(3 - 1)
  2. Simplify:                                                                                                             \displaystyle y' = 3x^2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Differentiation

Suppose you average 52 mi/h traveling on the highway. If you drive for 5 hours, how far will you travel? A. 260 miles B. 250 miles C. 350 miles D. 240 miles

Answers

if you average 52 mi/h for 5 hours you would travel about 260 miles
A. 260 miles. 52 per hour, so 52 times 5.

Which is greater, 0.5 or 2/3??

Answers

Find the average=.gr2ate2+0.5+ 23 3
Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD). 
 which  equals 3
Find the mean (arithmetic)-.gr^2ate^2+0.5+ 23 3
The LCM (least common multiple) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.=2grat

In other words:
0.5, 3/5, 0.65, 2/3
 Hope this helps
 So therefore, 2/3 is greater
0.5, 2/3 = 0.6So 2/3 is greater.Hope it helps and pls mark as the best answer. :-)
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