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weeeeeb [17]
2 years ago
13

What is the explicit formula for this geometric sequence with recursive formula

Mathematics
2 answers:
Klio2033 [76]2 years ago
8 0

Answer:

Option C

Step-by-step explanation:

Given is a geometric sequence.

The recursive formula is given as

a_n = \frac{1}{3} a_{n-1}

Hence ratio of nth term to n-1th term

=\frac{a_n}{a_{n-1} } =\frac{1}{3}

r=\frac{1}{3}

I term = a_1=-7

Hence explicit formula is

a_n = -7(\frac{1}{3} )^{n-1}

Option C is right

Nonamiya [84]2 years ago
6 0

C

generate the first few terms using the recursive formula

a_{2} = - 7 × \frac{1}{3} = - \frac{7}{3}

a_{3} = - \frac{7}{3} × \frac{1}{3} = - \frac{7}{9}

a_{4} = - \frac{7}{9} × \frac{1}{3} = - \frac{7}{27}

r = a_{2} / a_{1} = \frac{1}{3}


the n th term formula (explicit ) for a geometric sequence is

a_{n} = a_{1}r^{n-1} = - 7(\frac{1}{3})^(n - 1)


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