HOW TO FIND THE MISSING TERMS IN AN ARITHMETIC SEQUENCE

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

Formula to find nth term of an Arithmetic Sequence :

an = a + (n - 1)d

a----> nth term

a ----> first term

d ----> common difference

Example 1 :

Find 30th term in the arithmetic sequence given below.

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

Solution :

a = 10

d = a2a2

= 7 - 10

= -3

an = a + (n - 1)d

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

a30 = 10 + (30 - 1)(-3)

= 10 + 29(-3)

= 10 - 87

= -77

30th term is -77.

Example 2 :

Find 11th term in the arithmetic sequence given below.

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

Solution :

a = -3

d = a2a2

= -1/2 - (-3)

= -1/2 + 3

= (-1 + 6)/2

= 5/2

an = 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

11th 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

an = 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 :

a2 = 13

a + (2 - 1)d = 13

a + d = 13 ----(1)

a4 = 3

a + (4 - 1)d = 3

a + 3d = 3 ----(2)

(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

an = 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.

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