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Does someone know how to do this??

Does someone know how to do this??-example-1
User Rocketboy
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1 Answer

4 votes

Answer:

Explanation:

Question (1)

From the table showing arithmetic sequence,

First term of the sequence = 18

5th term of the sequence = -10

Explicit formula of an arithmetic sequence,


T_(n)=a+(n-1)d

For 5th term,

-10 = 18 + (5 -1)d

-10 = 18 + 4d

4d = -28

d = -7

Therefore, explicit formula for the table will be,


T_n = 18 + (n - 1)(-7)

= 18 - 7n + 7

= 25 - 7n


T_n=25-7n

Recursive formula →
T_n=T_(n-1)+d


T_n=T_(n-1)-7

Question (2),

From the table attached,

First term of the geometric sequence = 6

5th term = 96

Recursive formula of a geometric sequence =
a(r)^(n-1)

Here a = first term

r = common ratio

For 5th term from the table,

96 =
6(r)^(5-1)

r⁴ = 16

r =
\sqrt[4]{16}

r = 2

Therefore, explicit formula will be,


T_n=6(2)^(n-1)

Recursive formula will be,


T_n=T_(n-1)* (r)


T_n=2* T_(n-1)

User Ishara Amarasekera
by
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