Finding the nth term of an Arithmetic Sequence

What is the 5th term of the following arithmetic sequence?

4, 0, - 4, - 8, ...

• - 4

• 4

• - 12

• 12

Answer explanation

The sequence decreases by 4 each time. Starting from 4: 4 (1st), 0 (2nd), -4 (3rd), -8 (4th), and -12 (5th). Thus, the 5th term is -12.

What is the 5th term of the following arithmetic sequence?

6.6, 7.2, 7.8, 8.4, ...

• 0.6

• 9

• 8.6

• 9.6

Answer explanation

The common difference in the sequence is 0.6 (7.2 - 6.6). To find the 5th term, add 0.6 four times to the first term: 6.6 + 4(0.6) = 6.6 + 2.4 = 9. Thus, the 5th term is 9.

What is the 6th term of the following arithmetic sequence?

14, 19, 24, 29, ...

• 5

• - 5

• 34

• 39

Answer explanation

The sequence increases by 5 each time. Starting from 14, the 6th term is 14 + 5*5 = 39. Thus, the correct answer is 39.

What is the 6th term of the following arithmetic sequence?

- 15, - 22, - 29, - 36 ...

• 7

• - 7

• - 50

• - 57

Answer explanation

The sequence decreases by 7 each time. Starting from -15, the 6th term is calculated as -15 + 5*(-7) = -15 - 35 = -50. Thus, the 6th term is -50.

What is the 5th term of an arithmetic sequence whose first term is 7 and has a common difference of 4?

• - 13

• 23

• 27

• 27

Answer explanation

To find the 5th term of the arithmetic sequence, use the formula: a_n = a_1 + (n-1)d. Here, a_1 = 7, d = 4, and n = 5. Thus, a_5 = 7 + (5-1)4 = 7 + 16 = 23. The correct answer is 23.

What is the first term of an arithmetic sequence if its fifth term is - 1 and it has a common difference of 3?

• - 13

• - 11

• 11

• 13

Answer explanation

In an arithmetic sequence, the nth term is given by the formula: a_n = a_1 + (n-1)d. Here, a_5 = a_1 + 4(3) = -1. Solving for a_1 gives a_1 = -1 - 12 = -13. Thus, the first term is -13.

What is the first term of an arithmetic sequence if its fifth term is - 1 and its tenth term is 14?

• 13

• - 13

• 11

• - 11

Answer explanation

In an arithmetic sequence, the nth term is given by a_n = a + (n-1)d. We have a_5 = a + 4d = -1 and a_10 = a + 9d = 14. Solving these equations, we find a = -13. Thus, the first term is -13.

What is the first term of an arithmetic sequence whose fifth term is 16 and whose seventh term is 20?

• 8

• 10

• 12

• 18

Answer explanation

In an arithmetic sequence, the nth term is given by a_n = a + (n-1)d. Here, a_5 = a + 4d = 16 and a_7 = a + 6d = 20. Subtracting these gives 2d = 4, so d = 2. Substituting d back, a + 8 = 16, thus a = 8.

In the arithmetic sequence { 1, 5, 9, 13, ... }, which term is equal to 41 ?

• 9th term

• 10th term

• 11th term

• 12th term

Answer explanation

In the sequence, the nth term can be found using the formula: a_n = 1 + (n-1) * 4. Setting a_n = 41, we solve: 41 = 1 + (n-1) * 4, leading to n = 11. Thus, the 11th term is 41.

What is the eleventh term of an arithmetic sequence whose eighth term is - 27 and whose fifteenth term is - 55?

• 4

• - 4

• 39

• - 39

Answer explanation

In an arithmetic sequence, the nth term can be expressed as a_n = a_1 + (n-1)d. Given a_8 = -27 and a_15 = -55, we can find d. Solving gives d = -4. Thus, a_11 = a_8 + 3d = -27 + 3(-4) = -39.