Question

What is the 7th term in the geometric sequence described by this explicit formula? An=7•3(n-1)
A.15,309
B.823,543
C.729
D.5103

Answer 1

The 7th term of the geometric sequence described by this explicit formula $a_{n}=7*3^{(n-1)}$ is 5103 ⇒ answer D

Step-by-step explanation:

The explicit formula of nth term in the geometric sequence is

$a_{n}=a(r)^{n-1}$ , where

• a is the first term
• r is the common ratio between each two consecutive terms

∵ The explicit formula of a geometric sequence is $a_{n}=7*3^{(n-1)}$

∵ The explicit formula of nth term in the geometric sequence

   is $a_{n}=a(r)^{n-1}$

∴ a = 7 and r = 3

∵ We need to find the 7th term

∴ n = 7

- Substitute n by 7 in the formula

∴ $a_{7}=7*3^{(7-1)}$

∴ $a_{7}=7*3^{(6)}$

∵ $3^{(6)}=729$

∴ $a_{7}=7(729)$

∴ $a_{7}=5103$

The 7th term of the geometric sequence described by this explicit formula $a_{n}=7*3^{(n-1)}$ is 5103

Learn more:

You can learn more about geometric sequence in brainly.com/question/1522572

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