Generating Patterns and Illustrating Arithmetic Sequence
Studynote
Brief Introduction:
Recognizing and extending patterns are important skills needed for learning concepts related to
Sequence. Given at least the first 3 terms of a sequence you can easily find the next term in that and the
second term from the first term. You will find that either a constant number is added, subtracted,
multiplied, or divided to get the next term or a certain series of operations is performed to get the next
term.
The nth term that generates the pattern of a sequence
Examples:
1. Find the nth term that generates the pattern for the sequence 2,8,18, and 32
Solving a problem like this involves some guessing. Looking over the first 4 terms, see that each is twice
a perfect square.
a 1=¿2 = 2(1) = 2(1)²
a 2 = 8 = 2(4) = 2(2)²
a 3=18=2(9)=2(3))²
a 4=32=2(16)=2 (4)¿ ²
an = 2n
Answer: The nth term for the sequence 2,8,18,32, is an = 2n
2. Find the nth term that generates the pattern for the sequence 2, 3|8, 4|27, 5|64
a 1= 2 1+1
13
a2 = 3 =2+1
8 23
a3 = 4 = 3 + 1
27 33
a4 =5 =4+1
64 43
an = n + 1
n3
Answer: The nth term for the sequence 2, 3, 4 ,5 is an = n + 1
8 27 64 n3
3. Find the nth that generates the pattern for the sequence -2, 4, -8, 16, 32
The term -2, 4, -8, 16, 32 are powers of 2 and they alternate in sign.
a1 = -2 = (-2)1
a2 = 4 = (-2)2
Studynote
Brief Introduction:
Recognizing and extending patterns are important skills needed for learning concepts related to
Sequence. Given at least the first 3 terms of a sequence you can easily find the next term in that and the
second term from the first term. You will find that either a constant number is added, subtracted,
multiplied, or divided to get the next term or a certain series of operations is performed to get the next
term.
The nth term that generates the pattern of a sequence
Examples:
1. Find the nth term that generates the pattern for the sequence 2,8,18, and 32
Solving a problem like this involves some guessing. Looking over the first 4 terms, see that each is twice
a perfect square.
a 1=¿2 = 2(1) = 2(1)²
a 2 = 8 = 2(4) = 2(2)²
a 3=18=2(9)=2(3))²
a 4=32=2(16)=2 (4)¿ ²
an = 2n
Answer: The nth term for the sequence 2,8,18,32, is an = 2n
2. Find the nth term that generates the pattern for the sequence 2, 3|8, 4|27, 5|64
a 1= 2 1+1
13
a2 = 3 =2+1
8 23
a3 = 4 = 3 + 1
27 33
a4 =5 =4+1
64 43
an = n + 1
n3
Answer: The nth term for the sequence 2, 3, 4 ,5 is an = n + 1
8 27 64 n3
3. Find the nth that generates the pattern for the sequence -2, 4, -8, 16, 32
The term -2, 4, -8, 16, 32 are powers of 2 and they alternate in sign.
a1 = -2 = (-2)1
a2 = 4 = (-2)2
