If the interval is 15, and each row increases by 6, given that the 6th row has 700 seats, how many seats are there in the first row?
If there are 100 rows and there are 600 seats in the final row, how many are there in the first row if there are 8 more in each row?
If a sequence has 34 terms, the first row has 12, and the final row has 65, what is the common difference?
What is the common difference in a series that begins at 10 and ends at -50, if there are 14 terms?
If a sequence goes 41, 49, 57, 65, et cetera, taking 57 to be the first term, what is the value of the 4th and 14th terms?
In a sequence of 18 items, if the final item is 44 and the difference is 8, what is the first item?
The first item in a sequence of 38 items is 6 and the final item is 86, what is the common difference?
How many numbers are divisible by 5 between 42 and 193?
The 23rd term in a sequence that increases by 8 is 134. What is the 1st term?
A park has thirty-three trees in the 5th row of trees. If the trees increase by 4 every row, how many are there in the first row?
If the third term in a sequence is 6.5, and the fifth is 13.5 and the seventh is 20.5, what is the first term?
In 46 numbers, the last term is 12, and the difference is 3.4. What is the first term?
The 15th number in a sequence is 54, and the first is 30. What is the common difference?
How many numbers leave a remainder of 2 when divided by 7 in the range 4 to 104?
After counting by threes, the 54th number is 431. What was the 22nd number?
A sequence begins at 92, goes to 103, then to 114, and then 125 and continues along this line. If a sequence begins at 114 and ends at 499, how many terms are in the sequence?
The common difference in a sequence is -13. If the final term is -65 and the sequence is 12 items long, what is the 1st, 5th and 6th terms?
Beginning at 5, a sequence ends at 65. How many terms are there in the sequence if the common difference is 12?
20 is the 5th number in an evenly progressing sequence and 80 is the 10th. What is the first?
In 65 numbers, the final number is 64.1. If the sequence progresses by 2.1, what is the 10th term?
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solution 1
ReplyDeletefor this ap question we use the formula
A + (n-1)d
so
A + (6-1)6 = 700
A + (5*6) = 700
A + 30 = 700
A = 700-30
A = 670
There are 670 seats in the first row
note A represents the value of the first term
solution 2
ReplyDeleteusing the same approach as questions 1
A +(n-1)d
A +(100-1)8 = 600
A + (99*8) = 600
A + 792 = 600
A = 600 - 792
A = -192
a + (n -1 ) d = l
ReplyDeletewhere a = 12
n=34
l = 65
d = ?
so substuting values into the formula we get
12 + ( 34-1) d = 65
12 + 33 d = 65
45 d = 65
d = 65- 45
= 20
hey guys I am not positive so please feel free to correct me
Number 4
ReplyDeletefollowing all the steps from above
10 ( 14-1 ) d = 50
10 + 13 d = 50
23 d = 50
d = 2.17
a = 57
ReplyDeleted = 8
n = 4
so a[n] = a + (n-1 ) d
57 + (4-1)8
= 57 + 24
4 th term =81
continuing with number 5
ReplyDeletea [n] = a + (n-1) d
= 57 + (14-1) 8
= 57 + 104
14 th term = 161
number 6
ReplyDeletea + (n -1 ) d = l
a= ?
l=44
d=8
substuting values into the equation
a + ( 18 -1) 8 = 44
a + 136 = 44
a + 44 - 136
a = 44 - 136
a = -92
number 7
ReplyDeletea = 6
l = 86
d = ?
n= 38
a = (n-1) d = l
6 + ( 38-1) d = 86
6 + 37 d = 86
43 d = 86 - 43
d = 43
number 8
ReplyDeleted = 5
a = 42
l =193
n= ?
a + (n-1) d = l
42 + (n-1)5 = 195
42 + (n-1) = 193/5
42+ (n-1) = 38.6 -42
n-1 = -3.4
n = -3.4 + 1
n = -2.4
number 9
ReplyDeleted = 8
n = 23
a = ?
l= 134
l = a + (n-1) d
134 = a + (23 -1)8
134 = a + 22 * 8
134 = a + 176
a = 134 -176
a = -42
number 10
ReplyDeleted = 4
a = ?
l = 23
n =5
l = a + (n-1) d
33 = a + (5-1) 4
33 = a + 16
33-16 = a
a = 17
help with number 11
ReplyDeletenumber 12
ReplyDeletel = 12
d = -3.4
a = ?
n = 46
l = a + (n-1) d
12 = a (46 -1) 3.4
12 = a + 153
a = 12 -153
a = -141
number 13
ReplyDeleten = 15
a = 30
d = ?
l = 54
l = a + (n-1) d
54 = 30 + (15-1) d
54 -30 = ( 15-10 d
24 = (15-1) d
d =24/14
d = 1.7
number 14
ReplyDeleted = 7
n =?
l =104
a = 4
l = a + (n-1) d
104 = 4 + (n-1) 7
104-4 = (n-1) 7
100/7 = n-1
n = 14.3 + 1
n= 15.3