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A day full of math games & activities. Find one near you.
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.
Solution:
The n-th term of an arithmetic sequence is given by an = a + (n - 1)d
Given, a18 = 97
a + (18 - 1) d = 97
a + 17d = 97 -------------- (1)
Also, a20 = 281
a + (20 - 1) d = 281
a + 19 d = 281 ------------ (2)
Solving (1) and (2)
(2) - (1) we get, 19d - 17d = 184
2d = 184
d = 92
Now finding ist term a,
a + 17(92) = 97
a + 1564 = 97
a = -1467
To find n-th term,
an = -1467 + (n - 1)92
an = -1467 + 92n - 92
an = 92n - 1559
Therefore, the value of an = 92n - 1559.
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.
Summary:
The n-th term of the arithmetic sequence where a18 = 97 and a20 = 281 is 92n - 1559.
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