Answer:
1) Is the pattern an arithmetic sequence?
Yes it is
2)Identify a and d.
a = First term = 2
d = Common difference = 2
3) Write the 50th term of the sequence.
50th term = 100
4) Find the total number of logs in the first 10 rows.
= 1010 logs
Explanation:
Is the pattern an arithmetic sequence?
Yes it is
2) Identify a and d.
A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on,
The formula for arithmetic sequence =
an = a+ (n - 1)d
a = First term
d = Common difference
For the above question:
a = 2
d = Second term - First term
= 4 - 2
d = 2
3) Write the 50th term of the sequence.
Using the formula for arithmetic sequence
an = a+ (n - 1)d
a = 2
n = 50
d = 2
a50 = 2 + (50 - 1)2
= 2 + (49)2
= 2 + 98
= 100
The 50th term = 100
4)Find the total number of logs in the first 10 rows.
Sum of first n terms = n/2(a + l)
n = 10
a = first term = 2
We are told that there are 200 logs in the bottom row, hence:
l = last term = 200 logs
Hence,
Sn = 10/2×[ (2 + 200
= 5(202)
= 1010 logs