Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.
1 answer:
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Answer:
for n = 1, 2, . . . , 20.
Step-by-step explanation:
This is an arithmetic sequence, because the population is said to increase by 4 animals yearly. The formula for the nth term in an arithmetic sequence is given by:
where
is the nth term, [/tex]a_1[/tex] is the first term, n = 1, 2, . . . and d is the common difference.
Since they are currently 17, this implies that the first number in the population sequence will be 17. In order words, the first term is 17.
Since they increase by 4 yearly, then the common difference is 4.
Since it's for 20years, the n = 1, 2, . . ., 20. The explicit formula is therefore:
for n = 1, 2, . . . , 20.