The fifth term of an arithmetic sequence is 20 and the twelfth term is 41.
(a) (i) find the common difference.
(ii) find the first term of the sequence.
(b) calculate the eighty-fourth term.
(c) calculate the sum of the first 200 terms.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

one fourth of 9% = 2.25%

gavin is correct in saying : the equivalent quarterly interest rate would be

2.25%.

c(x)= 6x + 3

step-by-step explanation: