1. Select the first five terms in the arithmetic sequence an= 2 n , starting with n =1
A. ( 1 / 2 , 1/4 ,1/6, 1/8, 1/10)
B. ( 1 , 2 , 3 , 4 , 5 )
C. ( 3 , 4 , 5 , 6, 7 )
D. ( 2 , 4, 6 , 8, 10 )
My answer is D.
2. Select the first five terms in the geometric sequence an = ( 2 ) n-1 , starting with n =1 .
A. ( 2 ,4, 6, 8, 10)
B. (1, 2 , 4 , 8, 16 )
C. ( 1, 2, 4, 6, 8 )
D. ( 2, 4, 6 , 8 ,10 )
My answer is A.
3.Select the sum of the series symbol look like an E^5 k= 1 ^k 2
A. 55
B.56
C.200
D.225
My answer is D.
# 2. I meant for multiple choice
A. ( 2, 4 , 8 , 16 ,64 )
This is the answer I pick
James used the rulehe "add 2" to create a sequence. Then he used the "add 12" rule to create a second sequence. What are the first five terms in each sequence James created?
1. To find the first five terms in the arithmetic sequence with the formula an= 2n, starting with n = 1, we need to substitute n with the values 1, 2, 3, 4, and 5.
Substituting n = 1, the first term is a1 = 2(1) = 2.
Substituting n = 2, the second term is a2 = 2(2) = 4.
Substituting n = 3, the third term is a3 = 2(3) = 6.
Substituting n = 4, the fourth term is a4 = 2(4) = 8.
Substituting n = 5, the fifth term is a5 = 2(5) = 10.
Therefore, the first five terms in the arithmetic sequence are (2, 4, 6, 8, 10).
So, the correct answer is D.
2. To find the first five terms in the geometric sequence with the formula an = 2^(n-1), starting with n = 1, we need to substitute n with the values 1, 2, 3, 4, and 5.
Substituting n = 1, the first term is a1 = 2^(1-1) = 2^0 = 1.
Substituting n = 2, the second term is a2 = 2^(2-1) = 2^1 = 2.
Substituting n = 3, the third term is a3 = 2^(3-1) = 2^2 = 4.
Substituting n = 4, the fourth term is a4 = 2^(4-1) = 2^3 = 8.
Substituting n = 5, the fifth term is a5 = 2^(5-1) = 2^4 = 16.
Therefore, the first five terms in the geometric sequence are (1, 2, 4, 8, 16).
So, the correct answer is B.
3. The series given in symbolic notation is Σ(k=1 to 5) 2^k.
To find the sum of this series, we need to find the value of each term and then add them up.
Substituting k = 1, the first term is 2^1 = 2.
Substituting k = 2, the second term is 2^2 = 4.
Substituting k = 3, the third term is 2^3 = 8.
Substituting k = 4, the fourth term is 2^4 = 16.
Substituting k = 5, the fifth term is 2^5 = 32.
Now, we add up all the terms:
2 + 4 + 8 + 16 + 32 = 62.
Therefore, the sum of the series Σ(k=1 to 5) 2^k is 62.
So, the correct answer is not listed.