Find the 17th term in the arithmetic sequence in which a_6 is 101 and a_9 is 83

manudyent7

manudyent7

Answered question

2022-09-07

Find the 17th term in the arithmetic sequence in which a 6 is 101 and a 9 is 83

Answer & Explanation

Brooklynn Valencia

Brooklynn Valencia

Beginner2022-09-08Added 18 answers

n t h term of an arithmetic sequence {a,a+d,a+2d,........}, whose first term is a and difference between a term and its preceeding term is d, is a+(n−1)d.
As 6 t h term is 101, we have a+5d=101 and .......(1)
as 9 t h term is 83, we have a+8d=83. ......(2)
Subtracting (1) from (2), we get 3d=−18 i.e, d=−6
Putting this in (1), we get a−30=101 or a=131
Hence, 17 t h term is 131 + 16 × ( - 6 ) = 131 - 96 = 35

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