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Suppose that in a sequence a2 = 14, a4 = 26, a6 = 38, a8 = 50, and a10 = 62. Which of the following is the explicit formula for the sequence?
1. an = 2n + 6
2. an = 2n + 12
3. an = 6n + 2
4. an = 12n + 2

Respuesta :

apologiabiology
seems to be aritmetic
an=a1+d(n-1) is aritmetic
a1=fist term
d=comon difference
n=which term


a4-a2=2d where d is the common difference
26-14=12
12=2d
6=d
so
a2-6=a1
14-6=8

an=8+6(n-1)
expand
an=8+6n-6
an=6n+2
3rd option

3rd equation 'an = 6n + 2' is an explicit formula for the sequence

By hit and trial method (trying to put values of 'n' in options) :

a2 = 14, a4 = 26, a6 = 38, a8 = 50, and a10 = 62 {Given}

  • an = 2n + 6 implies

a2 = 2 (2) + 6 = 10 ; a4 = 2 (4) + 6 =14 ; a8 = 2 (8) + 2 = 18 ; a10 = 2 (10) + 6 = 26

These values don't equalise with the given values.

  • an = 2n + 12 implies

a2 = 2 (2) + 12 = 16 ; a4 = 2 (4) + 12 = 20 ; a8 = 2 (8) + 12 = 22 ;                                   a10 = 2 (10) + 12 = 32

These values don't equalise with the given values

  • an = 6n + 12 implies

a2 = 6 (2) + 2 = 12 + 2 = 14 ; a4 = 6 (4) + 2 = 24 + 2 = 26 ;                                          a8 = 6 (8) + 2 = 48 + 2 = 50 ; a10 = 6 (10) + 2 = 60 + 2 = 62

These values do equalise with the given values

  • an = 12n + 2

a2 = 12 (2) + 2 = 26 ; a4 = 12 (4) + 2 = 50 ; a8 = 6 (8) + 2 = 50 ; a10 = 12 (10) + 2 = 122

These values don't equalise with the given values

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