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Maths-

General

Easy

Question

Write explicit formula. $a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3$

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=4-7n.

Explanation:

We have given $a subscript n equals a subscript n minus 1 end subscript minus 7 comma a subscript 1 equals negative 3$

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 $a subscript n equals a subscript n minus 1 end subscript minus 7$
So, d = -7
Also, We have a₁ = -3
So, The explicit formula will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals negative 3 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 7 right parenthesis end cell row cell a subscript n equals 4 minus 7 n. end cell end table$
.

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