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otez555 [7]
2 years ago
9

Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the neares

t hundredth.
1.)a17 ≈ 123,802.31
2.)a17 ≈ 30,707.05
3.a17 ≈ 19,684.01
4.)a17 ≈ 216,654.05
Mathematics
2 answers:
Mashutka [201]2 years ago
8 0
The geometric sequence formula is expressed as an =  a1 * r^(n-1) where n is an integer. In this case, upon substitution, 150.06 = 16 * r^(4). extracting r, r is equal to 1.75. Hence the 17th term from the formula is equal to 123802.32.


Lunna [17]2 years ago
6 0

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the first term of a geometric sequence is 16 the fifth term of the sequence is 150.06.

a_1=16

a_5=150.06

The nth term of a geometric sequence is

a_n=a_1r^{n-1}                  .... (1)

The fifth term of the sequence is

a_5=a_1r^{5-1}

Substitute a_1=16 and a_5=150.06.

150.06=16r^{4}

Divide both sides by 16.

9.37875=r^{4}

(9.37875)^{\frac{1}{4}}=r

r\approx 1.75

Substitute n=17, a_1=16 and r=1.75 to find the 17th term.

a_{17}=16(1.75)^{17-1}

a_{17}=123802.31384

a_{17}\approx 123802.31

Therefore the correct option is 1.

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