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What is the nth term for each sequence below ?

1. 3, 4, 5, 6, 7, ...

2. 3, 5, 7, 9, 11, ...

3. 2, 4, 8, 16, 32, ..

2
by JpaulEncinas

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1. 3, 4, 5, 6, 7, ...

2. 3, 5, 7, 9, 11, ...

3. 2, 4, 8, 16, 32, ..

by JpaulEncinas

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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

1) a₁ = 3 d= 1 (common difference)

an = a₁ + (n-1) (d)

an = 3 + (n-1) (1)

an = 3 - 1 + n

an = 3 + 2n - 2

3) geometric sequence

common ratio, r = 4 a₁=2

an = a₁