How many terms are in the arithmetic sequence 7, 1, −5, …, −161?
1 answer:
Answer:
29
Step-by-step explanation:
The n th term of an arithmetic sequence is
• = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = 1 - 7 = - 5 - 1 = - 6 and a₁ = 7, = - 161, hence
7 - 6(n - 1) = - 161 ← solve for n
7 - 6n + 6 = - 161
13 - 6n = - 161 ( subtract 13 from both sides )
- 6n = - 174 ( divide both sides by - 6 )
n = 29
There are 29 terms in the sequence
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