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belka [17]
3 years ago
6

Find the first six terms of the sequence.

Mathematics
1 answer:
Levart [38]3 years ago
3 0
A(n) = a1 * r^(n-1)
a1 = first term = -8
r = common ratio = 5

a(2) = -8 * 5^(2-1)
a(2) = -8 * 5^1
a(2) = -40

a(3) = -8 * 5^(3 - 1)
a(3) = -8 * 5^2
a(3) = -8 * 25
a(3) = -200

a(4) = -8 * 5^(4 - 1)
a(4) = -8 * 5^3
a(4) = -8 * 125
a(4) = -1000

a(5) = -8 * 5^(5 - 1)
a(5) = -8 * 5^4
a(5) = -8 * 625
a(5) = -5000

a(6) = -8 * 5^(6-1)
a(6) = -8 * 5^5
a(6) = -8 * 3125
a(6) = -25,000

the first 6 terms are : -8, -40, -200, -1000,  -5000, -25,000
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3 years ago
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A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

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