Write the Recursive Formula for the given sequence.
1, 4, 16, 64, 256, ...
a(n+1) = a(n) * -4; a(1) = 1?
a(n+1) = a(n) * -3; a(1) = 1?
a(n+1) = a(n) * 4; a(1) = 1?
a(n+1) = a(n) * 3; a(1) = 1?
well, it is clear that you keep multiplying by 4, right?
That only leaves one choice
The recursive formula for the given sequence 1, 4, 16, 64, 256, ... is:
a(n+1) = a(n) * 4; a(1) = 1
The recursive formula for the given sequence can be found by observing the pattern in the sequence. Let's break down each option step by step:
1) a(n+1) = a(n) * -4; a(1) = 1:
To find subsequent terms in the sequence, each term is multiplied by -4. This means that to find the second term, we multiply the first term (1) by -4, which gives us -4. Similarly, to find the third term, we multiply the second term (-4) by -4, which gives us 16. So the recursive formula for this option is a(n+1) = a(n) * -4, where a(1) = 1.
2) a(n+1) = a(n) * -3; a(1) = 1:
Similar to the first option, this option also multiplies each term by a constant (-3). The second term would be (-3) * (1) = -3, and the third term would be (-3) * (-3) = 9. So the recursive formula for this option is a(n+1) = a(n) * -3, where a(1) = 1.
3) a(n+1) = a(n) * 4; a(1) = 1:
In this option, each term is multiplied by a constant (4). The second term would be (4) * (1) = 4, and the third term would be (4) * (4) = 16. So the recursive formula for this option is a(n+1) = a(n) * 4, where a(1) = 1.
4) a(n+1) = a(n) * 3; a(1) = 1:
In this option, each term is multiplied by a constant (3). The second term would be (3) * (1) = 3, and the third term would be (3) * (3) = 9. So the recursive formula for this option is a(n+1) = a(n) * 3, where a(1) = 1.
Given the sequence: 1, 4, 16, 64, 256, ...
Based on the pattern in the sequence, the correct recursive formula is a(n+1) = a(n) * 4, where a(1) = 1.