What is the #n th# term for an AP with a common difference of #-4.5?#

Answer 1

The nth term for an arithmetic progression (AP) with a common difference of -4.5 can be represented by the formula: ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, ( d ) is the common difference, and ( n ) is the term number. Given that the common difference is -4.5, the formula becomes: ( a_n = a_1 + (n-1)(-4.5) ).

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Answer 2

Eva Abramson

The sequence will be: #T_n = a-4.5n+4.5#

We know the general equation for nth term of an A.P.series is

#T_n =a+(n-1)d#

where #a# is the first term of the series and #d# is the common difference.

Now for the common difference (#d = -4.5 #) the sequence will be:

#T_n = a+(n-1)(-4.5)#

Simplifying gives: #T_n = a-4.5n+4.5#

The summation of all the terms will be:

#S_n =n/2(2a+(n-1)d)# where #d# is the common difference.

In your question #d=-4.5#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.