Answer:
248
Explanation:
Given the third and fourth terms of an arithmetic sequence are 13 and 18, you want the value of the 50th term.
Setup
The equation for the generic term of an arithmetic sequence is ...
an = a1 +d(n -1)
where an is the n-th term, a1 is the first term, and d is the common difference.
Using the given values, we can write two equations in the two unknowns, a1 and d:
- 13 = a1 +d(3 -1)
- 18 = a1 +d(4 -1)
Solution
Subtracting the first equation from the second, we have ...
(18) -(13) = (a1 +3d) -(a1 +2d)
5 = d . . . . simplify
Using this value in the first equation, we can find a1:
13 = a1 +2(5)
3 = a1 . . . . . . . . . . subtract 10
The 50th term is found from the formula above:
a50 = 3 +5(50 -1) = 3 +245 = 248
The 50th term of the sequence is 248.