2 years ago

What is the explicit formula for this sequence -7, -4, -1, 2, 5

Mathematics

1 answer:

ch4aika [34]2 years ago

6 0

$a_n=3n-10$

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An arithmetic sequence has this recursive formula: (a^1 =8, a^n= a^n-1 -6

eduard

Answer:

$a_n = 8 + (n - 1) (-6)$

Step-by-step explanation:

Given

$a_1 = 8$

Recursive: $a_{n} = a_{n-1} - 6$

Required

Determine the formula

Substitute 2 for n to determine $a_2$

$a_{2} = a_{2-1} - 6$

$a_{2} = a_{1} - 6$

Substitute $a_1 = 8$

$a_2 = 8 - 6$

$a_2 = 2$

Next is to determine the common difference, d;

$d = a_2 - a_1$

$d = 2 - 8$

$d = -6$

The nth term of an arithmetic sequence is calculated as

$a_n = a_1 + (n - 1)d$

Substitute $a_1 = 8$ and $d = -6$

$a_n = a_1 + (n - 1)d$

$a_n = 8 + (n - 1) (-6)$

Hence, the nth term of the sequence can be calculated using $a_n = 8 + (n - 1) (-6)$

3 0

2 years ago

Simplify.<br><br> 7−−√50−6−−√24

Pie

$7 + \sqrt{50} - 6 + \sqrt{24} \\ 7 + 5 \sqrt{2} - 6 + 2 \sqrt{6} \\ 1 + 5 \sqrt{2} + 2 \sqrt{6}$

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2 years ago

Given pre-image ABCDE. Which of the transformations resulted in image Point A'?

mihalych1998 [28]

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2 years ago

On a map where each unit represents one kilometer, two marinas are located at P(4,2) and Q(8,12). If a boat travels in a straigh

Slav-nsk [51]

Answer:

Step-by-step explanation:

draw a right angled triangle with the right angle in the bottom left

label P as the bottome left corner and write its coordinates next to it

do same with Q

the length of the triangle is 4 (8-4 = 4)

the height is 10 (12-2 = 10)

use pythagoras to work out the hypotenuse:

$\sqrt{4^{2}+10^{2}} =2\sqrt{29}$

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2 years ago

Select the correct answer

katen-ka-za [31]

its the 3rd one to be correct

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2 years ago