Answers

2016-06-15T03:39:48+08:00
Formula for this if your looking for a term is 
an = a1 + (n-1)d
where 
an is the value of the term
a1 is the first term
n is the exponent of the term
d is the common difference
from your example
1.) your looking for the 6th term, Using the formula
an = a1 + (n - 1 )d
where.
a1 = 3, n = 6 , d= 4-3 or 5-4 or 6-5 = 1
subs.
6n = 3 + (6-1) 1
6n = 8, so 6th term is 8
2.) same formula your still looking for 6th term
a1 = 3 , n = 6, d = 5-3 = 2
subs
6n = 3 + (6-1) 2
6n = 13 , so the 6th term is 13
3.) this is a geometric sequence
formula for geometric sequence is: An = ar^(n-1)
still the same your looking for the 6th term
a = 2
n = 6
if you notice the common ratio is 2 because from your given
2x2= 4, 4x2= 8, 8x2 =16 , 16x2 = 32
2,4,8,16,32
6n = 2(2)^(6-1)
6n = 64 , so the 6th is 64 

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  • Brainly User
2016-06-15T08:43:39+08:00
RULE FOR THE NTH TERM:
1)  a₁ = 3       d= 1 (common difference)
   
     an = a₁ + (n-1) (d)
     an = 3 + (n-1) (1)
     an = 3 - 1 + n
     an = n + 2

2)  a₁=3     d = 2
     an = 3 + (n-1) (2)
     an = 3 + 2n - 2
     an = 2n + 1

3)  geometric sequence
     common ratio, r = 4        a₁=2
 
     an = a₁  (r) ^{n-1}
     an = 2(2) ^{n-1}



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