To find the missing terms in the sequence, we have to understand the pattern first.
Types of sequence,
i) Arithmetic sequence
ii) Geometric sequence
iii) Special sequence
Arithmetic sequence :
If common difference is same, then the sequence is known as arithmetic progression. To find nth term of the arithmetic progression, we use the formula
an = a + (n - 1)d
Geometric sequence :
If common ratio is same, then the sequence is known as geometric progression. To find nth term of the geometric progression, we use the formula
an = arn - 1
Problem 1 :
Find the next three terms :
3, 10, 17, 24, 31, ____, ____, ____
Solution :
a = 3
d = 10 - 3 = 7
an = a + (n - 1)d
a6 = 3+(6-1)7 = 3+35 a6 = 38 |
a7 = 3+(7-1)7 = 3+42 a7 = 45 |
a8 = 3+(8-1)7 = 3+49 a8 = 52 |
So, next
three terms are 38, 45 and 52.
Problem 2 :
Find the 25th term :
53, 50, 47, 44, 41,…_____
Solution :
a = 53
d = 50 - 53 = -3
an = a + (n-1)d
a25 = 53 + (25-1)(-3)
= 53 - 72
a25 = -19
Hence, 25th term is -19.
Problem 3 :
Find the 20th term :
25, 40, 55, 70, 85,…_____
Solution :
a = 25
d = 40 - 25 = 15
an = a + (n - 1)d
a20 = 25 + (20 - 1)(15)
= 25 + 285
a20 = 310
Hence, 20th term is 310.
Problem 4 :
Find the 75th term
88, 81, 74, 67, 60,…_____
Solution :
d = 81 - 88 = -7
an = a + (n - 1)d
a75 = 88 + (75 - 1)(-7)
= 88 - 518
a75 = -430
Hence, 75th term is -430.
Determine if the sequence is arithmetic or geometric, and then find the given term.
Problem 5 :
Find the 11th term:
5, 3, 1, -1,…
Solution :
a = 5
d = 3 - 5 = -2
an = a + (n - 1)d
a11 = 5 + (11 - 1)(-2)
= 5 - 20
a11 = -15
Hence, 11th term is -15.
Problem 6 :
Find 23rd term of
0.1, 0.15, 0.2, 0.25,… ______
Solution :
a = 0.1
d = 0.15 - 0.1 = 0.05
an = a + (n - 1)d
a23 = 0.1 + (23 - 1)(0.05)
= 0.1 + 1.1
a23 = 1.2
Hence, 23rd term is 1.2.
Problem 7 :
Find 6th term:
25, 75, 225, 675,… ______
Solution :
a = 25
r = 75/25
r = 3
an = a ∙ rn-1
a6 = 25(3)6-1
= 25(3)5
= 25 × 243
a6 = 6075
Hence, 6th term is 6075.
Problem 8 :
Find 22nd term: -2, -5, -8, -11, -14,… ______
Solution :
a = -2
d = -5 - (-2) = -3
an = a + (n - 1)d
a22 = -2 + (22 - 1)(-3)
= -2 - 63
a22 = -65
Hence, 22nd term is -65.
Problem 9 :
Find 10th term: a1 = 320, r = 0.5
Solution :
a1 = 320, r = 0.5 = 1/2
an = a1 ∙ rn-1
a10 = 320 ∙ (1/2)10 -1
= 320(1/2)9
= 320/512
a10 = 0.625
Hence, 10th term is 0.625.
Problem 10 :
Find 50th term: -9, 2, 13, 24, 35,…
Solution :
a = -9
d = 2 - (-9) = 11
an = a + (n - 1)d
a50 = -9 + (50 - 1)(11)
= -9 + 539
a50 = 530
Hence, 50th term is 530.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM