If f(x) = 2x - 3, find f(-2).

Express the terms of the following sequence by giving a recursive formula.

MAXImum [283]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

3 years ago

✨20 points✨

Lostsunrise [7]

B

25,000 x (0.95)*8 means the interest changes every year and the interest is calculated of the annual rate

5 0

3 years ago

The equation ℎ = −162 + 32 + 9 gives the height of a ball, h, in feet above the ground, at t seconds after the ball is thrown up

Maru [420]

Answer:

time = 1secs

Max height = 25metres

Step-by-step explanation:

Let the equation that models the height of the ball be expressed as;

h(t) = −16t^2 + 32t + 9

t is the time in seconds

The velocity of the ball at its maximum height is zero i.e dh/dt = 0

dh/dt = -32t + 32

0 = -32t + 32

32t = 32

t = 32/32

t = 1 seconds

The ball will reach its maximum height after 1 seconds.

Get the maximum height reached. Substitute t = 1 into the modeled function;

h(t) = −16t^2 + 32t + 9

h(1) = −16(1)^2 + 32(1) + 9

h(1) = −16 + 32 + 9

h(1)= 16+9

h(1) = 25

Hence the maximum height reached is 25metres

4 0

3 years ago

Is 2/4 greater than 1/8

lord [1]

2/4 is greater than 1/8 because if you change 2/4 to a fraction with the same denominator it would be 4/8 and 1/8. So 2/4 is greater than 1/8

4 0

3 years ago

How do you graph -1/4 X. Squared

beks73 [17]

Answer:

Points at (0,0) and (4,-1)

Step-by-step explanation:

8 0

3 years ago