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avanturin [10]
3 years ago
6

A recursive rule for a geometric sequence is a1=8;an=3/4an−1 .

Mathematics
2 answers:
Lapatulllka [165]3 years ago
4 0

Answer:

The explicit rule for this sequence is; a_n = 8 \cdot(\frac{3}{4})^{n-1}

Step-by-step explanation:

Given the statement: A recursive rule for a geometric sequence is

a_1=8 and a_n =\frac{3}{4}a_{n-1}

for n= 2;

a_2= \frac{3}{4}a_{1}= \frac{3}{4} \cdot 8 = 6

Similarly for n = 3;

a_3 = \frac{3}{4}a_{2}= \frac{3}{4} \cdot 6 = \frac{9}{2}

Therefore, we get a geometric sequence i.e,

8 , 6 , \frac{9}{2}, .......

Now, to find the explicit rule for this geometric sequence:

A geometric sequence states that  a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r).

It is given by: a_n = a_1r^{n-1} where a_1 is the first term, r s the common ratio and n is the number of terms;

In the given sequence:  a_1 = 8, r = \frac{3}{4}

then, the explicit rule for this sequence is;

a_n = 8 \cdot(\frac{3}{4})^{n-1}

Illusion [34]3 years ago
3 0
8(3/4)^n-1 i hope this help....
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