Write expression for the nth term of sequence?

Question

5, 7, 9, 11 is the sequence.

i don't know the answer.. >__<
is it n^(2-1) ?
bleahh seems wrong.. xP please teach me!! thankss

for the sequence 1, 2, 4, 8... the answer was 2^(n-1) in the back of the book.. so yeah..
and the sequence 3, 2, 4/3, 8/9, was
3 × (2/3)^(n-1)
i understand why there's a 2/3, but i don't get why they had to multiply it by 3..

Answer 1

The sequence is 2n+3

2*1 + 3 = 5
2*2 + 3 = 7
2*3 + 3 = 9
2*4 + 3 = 11

For the last sequence, it's 3*(2/3)^(n-1) because the first term (n=1) is 3. If the series were just (2/3)^(n-1), the first term would be 1 [(2/3)^0 = 1], and the second would be 2/3 [(2/3)^1 = 2/3].

To derive that sequence, you'd note that each subsequent term is 2/3 times the previous (so you have something of the form (2/3)^n)... then multiply that by whatever constant value is needed to get the first term to match up for n=1. You could write 9/2*(2/3)^n, which is equivalent, instead.

Answer 2

Look at where you start is the best thing with sequences. So the first sequence answer would be 5+ something
Since the sequence increases by two, 5+2(N-1) or 3+2N works.

The third sequence had to start with three, since the first number that (2/3)^(n-1) generates is 1, you need the three to start the sequence.

Answer 3

Arithmetic Progression

Example: 5,7,9,11,...The 1st term = a = 5
The common difference = d =T2 - T1= 7-5=2

nth term of sequence = a + (n - 1) d
nth term of sequence = 5+(n-1)2
nth term of sequence=5+2n-2
nth term of sequence=2n+3

Geometric Progression:
Example:1,2,4,8,….The 1st term = a = 1
The common ratio = r = T2/T1 = 2/1=2

T n = a r^( n-1)
Tn =1*2^(n-1)
Tn = 2^(n-1)


Example:,3, 2, 4/3, 8/9….The 1st term = a = 3
The common ratio = r = T2/T1 = 2/3
T n = a r^( n-1)
Tn= 3 × (2/3)^(n-1)

QED

Answer 4

it extremely is an mathematics progression with first time period a = ninety 8, and consumer-pleasant enormous distinction d = -4 The formula for the nth time period is x_n = a + d(n-a million) {see link for rationalization} for this reason x_n = ninety 8 - 4(n-a million) =102 - 4n

Answer 5

n+2(i think)

Answer 6

2n + 3 works for me....