Sequences Test Practice Questions for University

Determine the 5th term of the geometric sequence with the first term 3 and common ratio 2.

If the sequence is defined by ( a_n = 2a_ + 1 ) and ( a_1 = 1 ), what is ( a_3 )?

What is the nth term of the arithmetic sequence with the first term 7 and common difference -2?

Find the sum of the first 10 terms of the geometric sequence 5, 15, 45, ...

What is the common ratio of the geometric sequence if the 4th term is 81 and the 7th term is 6561?

Calculate the 12th term of the arithmetic sequence 1, 4, 7, 10, ...

Determine the sum of the first 8 terms of the geometric sequence 1, 3, 9, 27, ...

What is the 6th term of the sequence defined by ( a_n = n^2 - 1 )?

Find the 8th term of the arithmetic sequence with the first term 2 and common difference 5.

What is the sum of the first 5 terms of the geometric sequence with the first term 4 and common ratio 1/2?

Determine the nth term of the sequence defined by ( a_n = 4n + 3 ).

What is the common difference of the arithmetic sequence if the 3rd term is 15 and the 7th term is 27?

Calculate the 9th term of the geometric sequence with the first term 7 and common ratio 2.

Find the sum of the first 25 terms of the arithmetic sequence 8, 12, 16, 20, ...

What is the nth term of the geometric sequence with the first term 5 and common ratio -2?

Determine the 4th term of the sequence defined by ( a_n = n^3 - 2n ).

What is the sum of the first 6 terms of the geometric sequence 10, 30, 90, ...

Calculate the 15th term of the arithmetic sequence with the first term 11 and common difference 3.

Find the common ratio of the geometric sequence if the 2nd term is 12 and the 5th term is 324.

What is the sum of the first 20 terms of the arithmetic sequence 5, 9, 13, 17, ...

Determine the 10th term of the geometric sequence with the first term 6 and common ratio 1/2.

What is the nth term of the sequence defined by ( a_n = 2n^2 + 3n - 1 )?

Calculate the sum of the first 12 terms of the arithmetic sequence 4, 10, 16, 22, ...

Find the 7th term of the geometric sequence with the first term 2 and common ratio 3.

What is the sum of the infinite geometric series 2 + 1 + 1/2 + 1/4 + ...?

Determine the common difference of the arithmetic sequence if the 6th term is 31 and the 12th term is 67.

What is the 5th term of the sequence defined by ( a_n = 5n - 3 )?

Calculate the 8th term of the arithmetic sequence with the first term 3 and common difference 7.

Find the sum of the first 6 terms of the geometric sequence with the first term 3 and common ratio 4.

What is the nth term of the arithmetic sequence with the first term 9 and common difference -4?

Determine the 5th term of the geometric sequence with the first term 8 and common ratio 1/3.

What is the sum of the first 10 terms of the arithmetic sequence 7, 11, 15, 19, ...

Calculate the 11th term of the geometric sequence with the first term 5 and common ratio -1.

Find the common ratio of the geometric sequence if the 3rd term is 24 and the 6th term is 192.

What is the sum of the first 15 terms of the arithmetic sequence with the first term 6 and common difference 8?

Determine the 9th term of the sequence defined by ( a_n = 3n^2 - 2n + 1 ).

What is the common difference of the arithmetic sequence if the 4th term is 22 and the 9th term is 42?

Calculate the 10th term of the geometric sequence with the first term 7 and common ratio 1/2.

Find the sum of the first 20 terms of the arithmetic sequence 12, 17, 22, 27, ...

What is the nth term of the geometric sequence with the first term 4 and common ratio -1/2?

Determine the 6th term of the sequence defined by ( a_n = n^2 + 4n + 4 ).

What is the sum of the first 7 terms of the geometric sequence with the first term 5 and common ratio 3?

Calculate the 8th term of the arithmetic sequence with the first term 10 and common difference -3.

Find the common ratio of the geometric sequence if the 4th term is 81 and the 8th term is 6561.

What is the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ...

Determine the 12th term of the geometric sequence with the first term 3 and common ratio 2.

What is the nth term of the sequence defined by ( a_n = 5n^2 + 2n - 1 )?

Calculate the sum of the first 15 terms of the arithmetic sequence 4, 8, 12, 16, ...

Find the 7th term of the geometric sequence with the first term 6 and common ratio 1/3.

What is the sum of the infinite geometric series 6 + 3 + 1.5 + 0.75 + ...?

Determine the common difference of the arithmetic sequence if the 5th term is 28 and the 10th term is 53.

What is the 9th term of the sequence defined by ( a_n = 2n^3 - n^2 + 3n - 1 )?

Calculate the 10th term of the arithmetic sequence with the first term 8 and common difference -2.

Find the sum of the first 6 terms of the geometric sequence with the first term 2 and common ratio 5.

What is the nth term of the arithmetic sequence with the first term 14 and common difference -7?

Determine the 5th term of the geometric sequence with the first term 10 and common ratio 1/4.