Write the nth term rule for the arithmetic sequence with a_5=17 and a_15=77

Gerardo Aguilar

Gerardo Aguilar

Answered question

2022-10-18

Write the nth term rule for the arithmetic sequence with a 5 = 17 and a 15 = 77

Answer & Explanation

Gael Irwin

Gael Irwin

Beginner2022-10-19Added 13 answers

Let a 1 , a n and d 0 denote the first , n t h and common difference for the Arithmetic Sequence in question.
Then, we know that, a n = a 1 + ( n - 1 ) d ... ... ... . . ( 1 )
Given that a 5 = 17 , so, taking n=5 in (1), we have,
a 1 + 4 d = 17 ... ... ... ... ... ( 2 )
Similarly, a 15 = 77 a 1 + 14 d = 77 ... ... ... ... ... . . ( 3 )
Solving ( 2 ) & ( 3 ) , d = 6 , and , a 1 = - 7
These, with (1) gives a n = 6 n - 13 , n

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