How many terms are in the following sequence? 14348907,

Ответ:

allenpaietonp9v8sv

17.01.2022

There are 16 terms in the sequence.

Step-by-step explanation:

The given sequence is

14348907, ..., 9, 3, 1

The first term of the sequence is

a_1=14348907

The last term of the sequence is l=1

The common ratio is $r=\frac{1}{3}$

The nth term of this sequence is;

$a_n=a_1(r)^{n-1}$

We plug in the common ratio and the first term to get;

$a_n=14348907(\frac{1}{3})^{n-1}$

The find the number of terms in the sequence , we plug in the last term of the sequence.

This implies that;

$1=14348907(\frac{1}{3})^{n-1}$

$\frac{1}{14348907}=(\frac{1}{3})^{n-1}$

$\Rightarrow 3^{-15}=3^{-(n-1)}$

Since the bases are the same, we equate the exponents;

-15=-(n-1)

15=n-1

15+1=n

n=16

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