Help with algebra, just a few questions. Urgent?

Question

2. what is the nth of the arithmetic sequence with the following first four terms?..3, 7, 11, 15

3. What is the nth term of the geometric sequence.. a1=2 and a3=18

4. What is the sum of the first 12 terms of the arithmetic sequence 2, 10, 18...

Answer 1

2. Given sequence 3 , 7 , 11 , 15-----------(1)

Say first term a1 = 3

Second term a2 = 7

Third term a3 = 11 and foyrth term a4 = 15

Now difference between the terms is 

d  = a2 - a1 = 7 - 3 = 4 (or)

d  = a3 - a2 = 11 - 7 = 4 (or)

d   = a4 - a3 = 15 - 11 = 4

The nth term of the arthimetic sequence is a(n) = a1 + (n-1)*d

a(n) = 3 + (n-1)*4

a(n) = 3 + 4n - 4

a(n) = 4n - 1

Therefore nth term is 4n -1

 

 

Answer 2

(3).

(4).

The sum of the first 12 terms of the arithmetic sequence 2, 10, 18... is 552.