-2, -12, -72, -432 find the 8th term
0.2, 1.6, 12.8, 102.4 find the 6th term
24, 12, 6, 3 find the 7th term
looks like all are geometric sequences
for a GS
term(n) = a r^(n-1)
I will do the 2nd one, you do the others
a = .2, r = 1.6/.2 = 8
term(6) = ar^5
= .2(8)^5
= .2(32768)
= 6553.6
To find the nth term of a sequence, we can use the formula:
nth term = first term * (common ratio)^(n-1)
For the first sequence: -2, -12, -72, -432, we notice that each term is obtained by multiplying the previous term by -6. Therefore, the common ratio is -6.
To find the 8th term, we substitute the values into the formula:
8th term = (-2) * (-6)^(8-1)
= (-2) * (-6)^7
= (-2) * (-279936)
= 559,872
Therefore, the 8th term of the sequence is 559,872.
For the second sequence: 0.2, 1.6, 12.8, 102.4, we notice that each term is obtained by multiplying the previous term by 8. Therefore, the common ratio is 8.
To find the 6th term, we substitute the values into the formula:
6th term = (0.2) * (8)^(6-1)
= (0.2) * (8)^5
= (0.2) * (32,768)
= 6,553.6
Therefore, the 6th term of the sequence is 6,553.6.
For the third sequence: 24, 12, 6, 3, we notice that each term is obtained by dividing the previous term by 2. Therefore, the common ratio is 1/2 or 0.5.
To find the 7th term, we substitute the values into the formula:
7th term = 24 * (0.5)^(7-1)
= 24 * (0.5)^6
= 24 * (0.015625)
= 0.375
Therefore, the 7th term of the sequence is 0.375.