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:

^{n}

^{n-2}·3

^{n-1}·3

^{n}·3

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

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

^{2}

^{2}

^{2}

^{2}

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

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 a_{10} - a_{3} = 21.

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

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

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

^{n}

^{n}

^{n+1}

^{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.

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