Answer:
- an = 12 + 7(n -1)
- a250 = 1755
Explanation:
The first figure has 12 line segments. The second figure has 19, 7 more than the first. The third figure has 7 more than that. The sequence of line segment counts is an arithmetic sequence with first term 12 and common difference 7. The formula for the general term of an arithmetic sequence can be used.
General term for sequence with first term a1 and common difference d:
an = a1 + d(n -1)
For the numbers in this problem, the equation is ...
an = 12 + 7(n -1)
__
The 250th term of the sequence is ...
a250 = 12 + 7(250 -1) = 1755