HOW TO FIND THE MISSING TERMS IN AN ARITHMETIC SEQUENCE

Using the formula for n^th term of an arithmetic sequence, we can find the missing terms.

Example 1 :

Find 30^th term in the arithmetic sequence given below.

10, 7, 4,.......

Solution :

a = 10

d = a₂ - a₂

= 7 - 10

= -3

a_n = a + (n - 1)d

Substitute n = 30, a = 10 and d = -3.

a₃₀ = 10 + (30 - 1)(-3)

= 10 + 29(-3)

= 10 - 87

= -77

30^th term is -77.

Example 2 :

Find 11^th term in the arithmetic sequence given below.

-3, -1/2, 2,.......

Solution :

a = -3

d = a₂ - a₂

= -1/2 - (-3)

= -1/2 + 3

= (-1 + 6)/2

= 5/2

a_n = a + (n - 1)d

Substitute n = 11, a = -3 and d = 5/2.

a₃₀ = -3 + (11 - 1)(5/2)

= -3 + 10(5/2)

= -3 + 5(5)

= -3 + 25

= 22

11^th term is 22.

Example 3 :

Find the missing term in the arithmetic sequence given below.

2, ___, 26

Solution :

a = 2

a₃ = 26

a + (3 - 1)d = 26

a + 2d = 26

Substitute a = 2.

2 + 2d = 26

Subtract 2 from both sides.

2d = 24

Divide both sides by 2.

d = 12

a_n = a + (n - 1)d

In the given arithmetic sequence, the missing term is second term. So, substitute n = 2, a = 2 and d = 12 in the formula above.

a₂ = 2 + (2 - 1)(12)

= 2 + (1)(12)

= 2 + 12

= 14

The missing term is 14.

Example 4 :

Find the missing term in the arithmetic sequence given below.

___, 13 , ___, 3

Solution :

(2) - (1) :

2d = -10

Divide both sides by 2.

d = -5

Substitute d = -5 in (1).

a + (-5) = 13

a - 5 = 13

Add 5 to both sides.

a = 18

First term = 18

a_n = a + (n - 1)d

In the given arithmetic sequence, another the missing term is third term. So, substitute n = 3, a = 18 and d = -5 in the formula above.

a₃ = 18 + (3 - 1)(-5)

= 18 + 2(-5)

= 18 - 10

= 8

Third term = 8

The missing terms are 18 and 8.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.