Find the formula for a_n for the arithmetic sequence a_5=190,a_10=115

Ariel Wilkinson

Ariel Wilkinson

Answered question

2022-09-05

Find the formula for a n for the arithmetic sequence a 5 = 190 , a 10 = 115

Answer & Explanation

Kyan Mcdonald

Kyan Mcdonald

Beginner2022-09-06Added 6 answers

From the given data we can easily calculate the difference d of the sequence.
If a 5 = a 1 + 4 d and a 10 = a 1 + 9 d , the we can calculate that:
a 10 - a 5 = 5 d , so: d = a 10 - a 5 5
d = 115 - 190 5 = - 75 5 = - 15
Now we can calculate a 1 using:
a 5 = a 1 + 4 d
190 = a 1 + 4 ( - 15 )
190 = a 1 - 60
a 1 = 250
So finally the n−th term is:
a n = 250 + ( n - 1 ) ( - 15 )
a n = 250 - 15 n + 15
a n = - 15 n + 265

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