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Maths-

General

Easy

Question

Write explicit formula. $a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56$

hint Hint:

A sequence is said to be arithmetic if the common difference is always constant.

The General formula of any AP is $a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d$ .

The correct answer is: a_n=77-21n

Explanation:

We have given $a subscript n equals a subscript n minus 1 end subscript minus 21 comma a subscript 1 equals 56$

We have to find the explicit formula of the given sequence.

Step 1 of 1:
We know that the recursive formula of an AP is $a subscript n equals a subscript n minus 1 end subscript plus d$ , where d is common difference.
Here we have $a subscript n equals a subscript n minus 1 end subscript minus 21$
So, d = -21
Also, We have a₁ = 56
So, The explicit formula will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 56 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 21 right parenthesis end cell row cell a subscript n equals 77 minus 21 n end cell end table$

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