Find the eighth term of each sequence. 144, 36, 9, 94,...

Write an explicit formula. Look for a simple addition or multiplication pattern between consecutive terms. Here, each term is 14 times the preceding term so the term (14)n or 14n is involved: 141,142,143,144, ... To obtain the original sequence, we multiply each term by 576 (since 144×4=576): 57641,57642,57643,57644, ... Hence, the explicit formula is: an=5764n The eighth term is: a8=57648=57665536 a8=91024 An easier way is to multiply 14 to each preceding term starting from 94: a5=94⋅14=916 a6=916⋅14=964 a7=964⋅14=9256 a8=9256⋅14=91024 Result: a8=91024

Ans:&nbsp;91024Solution : Use the previous number and divide it by 4&nbsp;2nd term:144÷4=36&nbsp;3rd term:36÷4=94th term:9÷4=945th term:94÷4=9166th term:916÷4=9647th term:964÷4=92568th term:9256÷4=91024

Write an explicit formula. Look for a simple addition or multiplication pattern between consecutive terms. Here, each term is 14 times the preceding term so the term (14)n or 14n is involved: 141,142,143,144, ... To obtain the original sequence, we multiply each term by 576 (since 144×4=576): 57641,57642,57643,57644, ... Hence, the explicit formula is: an=5764n The eighth term is: a8=57648=57665536 a8=91024 An easier way is to multiply 14 to each preceding term starting from 94: a5=94⋅14=916 a6=916⋅14=964 a7=964⋅14=9256 a8=9256⋅14=91024 Result: a8=91024

Ans:&nbsp;91024Solution : Use the previous number and divide it by 4&nbsp;2nd term:144÷4=36&nbsp;3rd term:36÷4=94th term:9÷4=945th term:94÷4=9166th term:916÷4=9647th term:964÷4=92568th term:9256÷4=91024

Resolved: "Find the eighth term of each sequence. 144,..."

Ronnie Baur

Answered question

2021-12-02

Find the eighth term of each sequence. 144, 36, 9,

\frac{9}{4}

,...

Answer & Explanation

Sculd1987

Beginner2021-12-03Added 19 answers

Write an explicit formula. Look for a simple addition or multiplication pattern between consecutive terms.
Here, each term is

\frac{1}{4}

times the preceding term so the term

{(\frac{1}{4})}^{n} or \frac{1}{4^{n}}

is involved:

\frac{1}{4^{1}}, \frac{1}{4^{2}}, \frac{1}{4^{3}}, \frac{1}{4^{4}}

, ...
To obtain the original sequence, we multiply each term by 576 (since

144 \times 4 = 576

\frac{576}{4^{1}}, \frac{576}{4^{2}}, \frac{576}{4^{3}}, \frac{576}{4^{4}}

, ...
Hence, the explicit formula is:

a_{n} = \frac{576}{4^{n}}

The eighth term is:

a_{8} = \frac{576}{4^{8}} = \frac{576}{65536}

a_{8} = \frac{9}{1024}

An easier way is to multiply

\frac{1}{4}

to each preceding term starting from

\frac{9}{4}

a_{5} = \frac{9}{4} \cdot \frac{1}{4} = \frac{9}{16}

a_{6} = \frac{9}{16} \cdot \frac{1}{4} = \frac{9}{64}

a_{7} = \frac{9}{64} \cdot \frac{1}{4} = \frac{9}{256}

a_{8} = \frac{9}{256} \cdot \frac{1}{4} = \frac{9}{1024}

Result:

a_{8} = \frac{9}{1024}

2022-05-31

Ans: $\frac{9}{1024}$

Solution : Use the previous number and divide it by 4

2nd term:144 $\div$ 4=36

3rd term:36 $\div$ 4=9

4th term:9 $\div$ 4= $\frac{9}{4}$

5th term: $\frac{9}{4}$ $\div$ 4= $\frac{9}{16}$

6th term: $\frac{9}{16}$ $\div$ 4= $\frac{9}{64}$

7th term: $\frac{9}{64}$ $\div$ 4= $\frac{9}{256}$

8th term: $\frac{9}{256}$ $\div$ 4= $\frac{9}{1024}$

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