Explicit: y=5(3 
x
 )​

Recursive: 
n
th
 value 
=
previous value
⋅
3
Recursive: n 
th
  value =previous value⋅3​

​The value of term number 
6
6​ is 
3645
3645​ and the sequence is being tripled​ at each step. ​Use one of the equations to find the value of term number 
7
7​.
Preview


We are given two forms of an equation for a sequence: **explicit** and **recursive**, and the sequence triples at each step.

### Information Given:
- The value of term \( n = 6 \) is 3645.
- The sequence triples at each step.

### Recursive Formula:
The recursive formula can be used to find the next term:
\[
a_n = a_{n-1} \times 3
\]
Where:
- \( a_n \) is the \( n \)-th term.
- \( a_{n-1} \) is the previous term.

We know \( a_6 = 3645 \), so to find \( a_7 \) using the recursive formula:
\[
a_7 = a_6 \times 3 = 3645 \times 3 = 10,935
\]

Thus, the value of the 7th term is \( 10,935 \).

### Explicit Formula:
The explicit formula for this geometric sequence is given by:
\[
y = 5 \times 3^x
\]
To find the 7th term, we substitute \( x = 7 - 1 = 6 \) (since \( x \) represents the position minus 1):
\[
y = 5 \times 3^6 = 5 \times 729 = 3645
\]
Then for the 7th term:
\[
y = 5 \times 3^7 = 5 \times 2187 = 10,935
\]

Both methods confirm the 7th term is \( 10,935 \).

Would you like more details or have any further questions?

---

Here are 5 related questions for you to explore:
1. What is the 8th term of this sequence using the recursive method?
2. Can you derive the explicit formula for a different geometric sequence?
3. How does the value of the common ratio affect the growth of the sequence?
4. What is the sum of the first 7 terms in this sequence?
5. How can you express this sequence in summation notation?

**Tip**: For geometric sequences, the ratio between consecutive terms stays constant.

Explicit: y = 5(3^x)
Recursive: nth value = previous value ⋅ 3
The value of term number 6 is 3645 and the sequence is being tripled at each step. Use one of the equations to find the value of term number 7.

Learn how to find the 7th term in a geometric sequence where each term triples. The value of the 6th term is 3645. Use both recursive and explicit formulas to find the next term, with step-by-step solutions. Ideal for students in Grades 9-11 studying geometric progressions and sequences.

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Recursive: n th value

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