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Sagot :
a. The formula for the nth term of the given arithmetic sequence is -
[tex]a_n[/tex] = 6(1 - n).
b. The 11th term of the given Geometric sequence is -5120.
a. We are the given set of numbers 12, 6, 0,... which is in arithmetic sequence with first term [tex]a_1[/tex] = 12 and the common difference
d = 12 - 6 = 6 - 0 = 6
Hence, d = 6.
We have to find the formula for the nth term of the given arithmetic sequence.
the formula to find the nth term in Geometric Progression is
[tex]a_n=a_1[/tex] + d(n−1)
Substituting the values [tex]a_1[/tex] = 12 and d = 6, we will get,
[tex]a_n[/tex] = 12 + 6(n - 1)
[tex]a_n[/tex] = 12 + 6n -6
[tex]a_n[/tex] = 6 - 6n
[tex]a_n[/tex] = 6(1 - n)
Hence, the formula for the nth term of the given arithmetic sequence is [tex]a_n[/tex] = 6(1 - n).
b. We are the given set of numbers -5,-10,-20,-40, which is in Geometric Sequence with first term [tex]a_1[/tex] = - 5 and the common ratio -
[tex]r=\frac{-40}{-20}=\frac{-20}{-10}=\frac{-10}{-5}=2[/tex]
hence, r = 2
the formula to find the nth term in Geometric Progression is
[tex]a_n=a_1 \cdot r^{n-1}[/tex]
Now we will find the 11th term in the given geometric sequence.
Use now [tex]a_1[/tex] = -5 and r = 2 and n = 11 in the formula as follows-
[tex]a_n=a_1 \cdot r^{n-1}[/tex]
[tex]a_{11}= -5 \cdot(2)^{11-1}[/tex]
[tex]a_{11}=-5 \cdot(2)^{10}[/tex]
[tex]a_{11}=-5 \cdot 1024[/tex]
[tex]a_{11}[/tex] = - 5120
Hence, the 11th term of the given Geometric sequence is -5120.
Read more about Sequences and series :
brainly.com/question/6561461
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