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What is the explicit formula for the sequence 9, 1, -7, -15?

Answer 1

Madelyn Anderson

17 - 8n

This is an #color(blue)" Arithmetic sequence " #

The standard sequence is:

a,a+d,a+2d,a+3d, ................ ,a + (n-1)d

where a is the 1st term , d the common difference and a + (n-1)d , the nth term.

here a = 9 , d = 1 -9 = -7-1 = -8

The nth term formula which allows any term in the sequence to be found is :

a + (n-1)d = 9 - 8(n-1) = 9 - 8n + 8 = #color(red)(|bar(ul(color(white)(a/a)color(black)( 17 - 8n )color(white)(a/a)|)))#

check 1st term (n=1) = 17 - 8(1) = 17-8 = 9

2nd term (n=2) = 17 - 8(2) = 17-16 = 1 etc.

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Answer 2

Anna Allen

The explicit formula for the sequence (9, 1, -7, -15) is given by:

[ a_n = 9 - 8n ]

Where (a_n) represents the (n)th term in the sequence.

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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.