Find the common difference, d, in the arithmetic sequence defined by the formula a_n=−1n/2+6

sorrowandsongto

sorrowandsongto

Answered question

2022-10-31

Find the common difference, d, in the arithmetic sequence defined by the formula a n = - 1 2 n + 6

Answer & Explanation

Theresa Wade

Theresa Wade

Beginner2022-11-01Added 9 answers

In any A.P., let us note that, T n + 1 - T n = d ... [ T n is n t h term ]
In our Example, d = a n + 1 - a n = { - 1 2 ( n + 1 ) + 6 } - { - 1 2 n + 6 } = - 1 2 .
There is still a short-cut.
In the Usual Notation,
T n = a + ( n - 1 ) d = d n + ( a - d ) = d n + b , say, b = a - d
So, d = the co-eff. of n d = - 1 2 .

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