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How do you write a rule for the nth term of the arithmetic sequence given a20 = 240, a15 = 170?
Solution:
The nth term an of an arithmetic sequence with a1 as the first term and d as the common difference
an = a1 + (n - 1)d
a20 = a1 + 19d = 240 --- (1)
a15 = a1 + 14d = 170 --- (2)
Subtracting equation (2) from (1)
⇒ 5d = 70
Divide both sides by 5
⇒ d = 14
Substituting the value of d in equation 2
⇒ a1 + 14 (14) = 170
⇒ a1 + 196 = 170
⇒ a1 = 170 - 196
⇒ a1 = -26
So we get,
⇒ an = -26 + (n - 1)(14)
⇒ an = -26 + 14n - 14
⇒ an = 14n - 40
Therefore, a rule for the nth term of the arithmetic sequence is an = 14n - 40.
How do you write a rule for the nth term of the arithmetic sequence given a20 = 240, a15 = 170?
Summary:
The rule for the nth term of the arithmetic sequence given a20 = 240, a15 = 170 is an = 14n - 40.
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