Solve each equation for the variable:

1. Find the n-th term of the sequence (n ≥ 1) for the following sequence:


















2. Find the n-th term of the sequence (n ≥ 1) for the following sequence:



-3ⁿ


(-1)^n-2·3


(-1)^n-1·3


(-1)ⁿ·3





3. Find the n-th term of the sequence (n ≥ 1) for the following sequence:

1, 9, 25, 49, 81...

(n-1)²

(n)²

(2n+1)²

(2n-1)²




4. Select the correct first four terms of the arithmetic sequence a_n, n ≥ 1, with a₁ = 7 and common difference d = 2.

7, 9, 11, 13


7, 5, 3, 1


7, 10, 13, 16


7, 9, 7, 9





5. Select the correct first four terms of the arithmetic sequence a_n, n ≥ 1, with:



















6. Find the common difference of the arithmetic sequence a_n, n ≥ 1, if a₁₀ - a₃ = 21.

2


3


4


5





7. Find the second term of the following geometric sequence:

a, b, 24, 36, 54.....

b = 12


b = 14


b = 16


b = 18





8. What is the n-th term of the geometric sequence a_n, n ≥ 1, if a₁ = 2 and a_n+1 = 3a_n ?

3ⁿ


2·3ⁿ


2·3ⁿ⁺¹


2·3^n-1




9. a_n, n ≥ 1, is an arithmetic sequence, and b_n, n ≥ 1, is a geometric sequence:

a_n: 2, 4, 6, 8...
b_n: 2, 4, 8, 16...

c_n is a sequence that results by multiplying the terms of a_n and b_n: c_n= a_n·b_n.

Calculate n, if c_n = 2048n.

n = 10


n = 12


n = 8


n = 9




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