FIND THE MISSING TERMS IN THE SEQUENCE

Problem 1 :

Find the next three terms :

3, 10, 17, 24, 31, ____, ____, ____

Solution :

a = 3

d = 10 - 3 = 7

a_n = a + (n - 1)d

So, next three terms are 38, 45 and 52.

Problem 2 :

Find the 25^th term :

53, 50, 47, 44, 41,…_____

Solution :

a = 53

d = 50 - 53 = -3

a_n = a + (n-1)d

a₂₅ = 53 + (25-1)(-3)

= 53 - 72

a₂₅ = -19

Hence, 25^th term is -19.

Problem 3 :

Find the 20^th term :

25, 40, 55, 70, 85,…_____

Solution :

a = 25

d = 40 - 25 = 15

a_n = a + (n - 1)d

a₂₀ = 25 + (20 - 1)(15)

= 25 + 285

a₂₀ = 310

Hence, 20^th term is 310.

Problem 4 :

Find the 75^th term 

88, 81, 74, 67, 60,…_____

Solution :

d = 81 - 88 = -7

a_n = a + (n - 1)d

a₇₅ = 88 + (75 - 1)(-7)

= 88 - 518

a₇₅ = -430

Hence, 75^th term is -430.

Determine if the sequence is arithmetic or geometric, and then find the given term.

Problem 5 :

Find the 11^th term:

5, 3, 1, -1,… 

Solution :

a = 5

d = 3 - 5 = -2

a_n = a + (n - 1)d

a₁₁ = 5 + (11 - 1)(-2)

= 5 - 20

a₁₁ = -15

Hence, 11^th term is -15.

Problem 6 :

Find 23^rd term of 

0.1, 0.15, 0.2, 0.25,… ______

Solution :

a = 0.1

d = 0.15 - 0.1 = 0.05

a_n = a + (n - 1)d

a₂₃ = 0.1 + (23 - 1)(0.05)

= 0.1 + 1.1

a₂₃ = 1.2

Hence, 23^rd term is 1.2.

Problem 7 :

Find 6^th term:

25, 75, 225, 675,… ______

Solution :

a = 25

r = 75/25

r = 3

a_n = a ∙ r^n-1

a₆ = 25(3)^6-1

= 25(3)⁵

= 25 × 243

a₆ = 6075

Hence, 6^th term is 6075.

Problem 8 :

Find 22^nd term: -2, -5, -8, -11, -14,… ______

Solution :

a = -2

d = -5 - (-2) = -3

a_n = a + (n - 1)d

a₂₂ = -2 + (22 - 1)(-3)

= -2 - 63

a₂₂ = -65

Hence, 22^nd term is -65.

Problem 9 :

Find 10^th term: a₁ = 320, r = 0.5

Solution :     

a₁ = 320, r = 0.5 = 1/2

a_n = a₁ ∙ r^n-1

a₁₀ = 320 ∙ (1/2)^{10 -1}

= 320(1/2)⁹

= 320/512

a₁₀ = 0.625

Hence, 10^th term is 0.625.

Problem 10 :

Find 50^th term: -9, 2, 13, 24, 35,…

Solution : 

a = -9

d = 2 - (-9) = 11

a_n = a + (n - 1)d

a₅₀ = -9 + (50 - 1)(11)

= -9 + 539

a₅₀ = 530

Hence, 50^th term is 530.