Take the sequence in 1a
The 10th term is 31
The 20th is 61
If you wanted to find these by continuing the series, you'd have to add 3 to the last number in the series, then 3 more, then 3 more, until you reach the 20th term. By this point, you will have added 3 to the first term 19 times. That's where the formula comes from. So here,
a = 4, the first term
n = 20, the number of the term we need
d = 3, how much we're adding each time between one term and the next
Then, to get the 20th term,
4 + (20 - 1) • 3 = 4 + (19 • 3) = 4 + 57 = 61
Answers
The 10th and 20th terms of each sequences are
a. 31; 61
b. 48; 98
c. 47; 97
(in <em>c</em>, you're adding the same <em>d</em> as in the sequence above, but your first term is one unit less)
d. -25; -75
(same thing as before, but now, <em>d</em> is negative)
e. 11.5; 16.5
(with <em>d</em>=1/2 or 0.5)
f. 6+1/2; 8+1/2
Use these to check your answers after applying the formula, but know that I calculated on the fly and didn't check these.
We know that the sum of arc ND and arc ML divided by 2 is equivalent to 6x + 23.
Thus, we can form an equation:
6x + 23 = (11x + 8 + 3x + 14)/2
Simplify:
6x + 23 = (14x + 22)/2
Simply again:
6x + 23 = 7x + 11
Subtract 6x from both sides:
23 = x + 11
Subtract 11 from both sides
x = 12
Option A, or x = 12
-T.B.
$12.50 because you would divide 50 and 4
5/4 x 22/45
110/ 180
11/18
