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Pie
3 years ago
15

100 POINTS! PLEASE HELP ASAP!

Mathematics
2 answers:
vampirchik [111]3 years ago
6 0

Question #1:

Since the common ratio is -2 that means each term is going to be multiplied by -2 to get the next term.

First term: -8

Second term: -8 * -2 = 16

Third term: 16 * -2 = -32

Fourth term: -32 * -2 = 64

Therefore, the first 4 terms of the geometric sequence are -8, 16, -32, 64

Question #2:

It gives an equation to follow to solve for each term of the sequence. We can solve for each term till we get to the 4th term.

Second term:

a2 = 2(5) + 3

a2 = 10 + 3

a2 = 13

Third term:

a3 = 2(13) + 3

a3 = 26 + 3

a3 = 29

Fourth term:

a4 = 2(29) + 3

a4 = 58 + 3

a4 = 61

Therefore, the fourth term of the sequence is 61.

Question #3:

a5 just means that we are going to find the fifth term of the sequence.

Second term:

a2 = -3(2) + 2

a2 = -6 + 2

a2 = -4

Third term:

a3 = -3(-4) + 2

a3 = 12 + 2

a3 = 14

Fourth term:

a4 = -3(14) + 2

a4 = -42 + 2

a4 = -40

Fifth term:

a5 = -3(-40) + 2

a5 = 120 + 2

a5 = 122

Therefore, the fifth term of the sequence is 122.

Best of Luck!

anygoal [31]3 years ago
4 0

Answer:

<u>PICTURE #1</u>

<u />a_1 = 5\\a_2 = 2a__(n-1) + 3

<u>Step 1:  Solve for </u>a_2

a1 = 5

a_2 = 2a___n-1\\ +3

a_2=2a__(2-1) + 3

a_2 = 2a_1 + 3

a_2 = 2(5) + 3

a_2 = 10 + 3\\

a_2 = 13

<u>Step 2:  Solve for </u>a_3

a_2 = 13

a_3 = 2a__(3-1) + 3

a_3 = 2a_2 + 3

a_3 = 2(13) + 3

a_3 = 26 + 3

a_3 = 29

<u>Step 3:  Solve for </u>a_4

a_3 = 29

a_4 = 2a__(4-1) + 3

a_4 = 2a_3 + 3

a_4 = 2(29) + 3

a_4 = 58 + 3

a_4 = 61

The fourth terms is:  a_4 = 61

<u>PICTURE #2</u>

<u></u>a_1 = 2\\a_2 = -3a__(n - 1) + 2

<u>Step 1:  Find </u>a_2

a_2 = -3a_1 + 2

a_2 = -3(2) + 2

a_2 = -6 + 2

a_2 = -4

<u>Step 2:  Find </u>a_3

a_3 = -3a_2 + 2

a_3 = -3(-4) + 2\\

a_3 = 12 + 2

a_3 = 14

<u>Step 3:  Find </u>a_4

a_4 = -3a_3 + 2

a_4 = -3(14) + 2

a_4 = -42 + 2

a_4 = -40

<u>Step 4:  Find </u>a_5

a_5 = -3a_4 + 2

a_5 = -3(-40) + 2\\

a_5 = 120 + 2

a_5 = 122

Answer:  The fifth term for the second picture is -> a_5 = 122

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