What is the 7th term of the sequence gn = gn−1 · (−2), if g3 = 20 ?
The sequence is generated by multiplying each term by -2. Given g3 = 20, we can find g4 by multiplying 20 by -2:
g4 = 20 * (-2) = -40
We can continue this process to find subsequent terms of the sequence:
g5 = -40 * (-2) = 80
g6 = 80 * (-2) = -160
g7 = -160 * (-2) = 320
Therefore, the 7th term of the sequence is 320.
To find the 7th term of the sequence gn = gn−1 · (−2), given that g3 = 20, we need to use the recursive formula to calculate each term step by step.
1. Start with the given value of g3 = 20.
2. Use the recursive formula gn = gn−1 · (−2) to find the next term.
g4 = g3 · (−2) = 20 · (−2) = -40
3. Repeat step 2 to find the next term.
g5 = g4 · (−2) = -40 · (−2) = 80
4. Repeat step 2 to find the next term.
g6 = g5 · (−2) = 80 · (−2) = -160
5. Repeat step 2 to find the next term.
g7 = g6 · (−2) = -160 · (−2) = 320
Therefore, the 7th term of the sequence is g7 = 320.