How do you find the nth term rule for the sequence 1, 2, 4, 8, 16, 32, 64?

To find the nth term rule for the sequence 1, 2, 4, 8, 16, 32, 64, we first need to identify the pattern in the sequence. Each term in the sequence is produced by multiplying the previous term by 2.

Let’s break it down:

• The first term (n=1) is 1 = 2⁰
• The second term (n=2) is 2 = 2¹
• The third term (n=3) is 4 = 2²
• The fourth term (n=4) is 8 = 2³
• The fifth term (n=5) is 16 = 2⁴
• The sixth term (n=6) is 32 = 2⁵
• The seventh term (n=7) is 64 = 2⁶

From this breakdown, we can see that the nth term of the sequence can be expressed as:

nth term = 2^(n-1)

This formula shows that for any term in the sequence, we take 2 raised to the power of (n-1). For instance:

• If n=1, then the term is 2^(1-1) = 2⁰ = 1
• If n=2, then the term is 2^(2-1) = 2¹ = 2
• If n=3, then the term is 2^(3-1) = 2² = 4
• If n=7, then the term is 2^(7-1) = 2⁶ = 64

This consistent pattern confirms that the nth term rule for the sequence is indeed 2 raised to the power of (n-1).