Write the nth term rule for the sequence 5/2,11/6,7/6,1/2,−1/6,...

gemuntertjx

gemuntertjx

Answered question

2022-09-08

Write the nth term rule for the sequence 5 2 , 11 6 , 7 6 , 1 2 , - 1 6 , ...

Answer & Explanation

detegerex

detegerex

Beginner2022-09-09Added 16 answers

In { 5 2 , 11 6 , 7 6 , 1 2 , - 1 6 ... } , let us make denominator common. As GCD is 6, we can write the series as
{ 15 6 , 11 6 , 7 6 , 3 6 , - 1 6 ... }
We observe that numerators form the series
{15,11,7,3,−1,...} which form an arithmetic series with first term a as 15 and common difference d between a term annd its preceding term is 12−15=−4. Hence, nth term of this series is a+(n−1)d i.e. 15 + ( n - 1 ) × ( - 4 ) = 15 - 4 n + 4 = 19 - 4 n
Hence n t h term of the series is 19 - 4 n 6

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