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Nady [450]
3 years ago
15

What is the 19th term of a geometric sequence where a1=8 and a9=360. Round the common ratio and 19th term to the nearest hundred

th.
REALLY need help on this one please please.
Mathematics
2 answers:
asambeis [7]3 years ago
8 0

<u>Answer:</u>

r = 1.6

a19 = 37800

<u>Step-by-step explanation:</u>

First term a_1 = 8 and a_9 = 360 of a geometric sequence and we are to find the 19th term along with the common ratio for this sequence.

We know that the general term of a Geometric Sequence is given by:

a_n= a \cdot r^{n-1}

where a_n is the nth term, a is the first term, n is the number of terms and r is the common ratio.

Substituting the given values in the above formula to get:

360 = (8)*(r)^(9-1)

360 = 8*(r^8)

r^8 = \frac{360}{8}

r^8 = 45

r = 1.6

Finding the 19th term:

a_n= a \cdot r^{n-1}

a_{19}= 8 \cdot 1.6^{19-1}

a19 = 37800

denpristay [2]3 years ago
7 0

Answer:

Step-by-step explanation:

a_{1} = 8\\a_{9} = 360 = a_{1} \cdot r^9 = 8 \cdot r^9\\r = \sqrt[9]{\frac{360}{9} }  \cong 1.53

By the formula of a geometric series:

S_{n} = a \cdot \frac{1-r^n}{1-r} => S_{19} = 8 \cdot \frac{1-1.53^{19}}{1-1.53}  = 6091.54

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