In an arithmetic progression the sum of the fifth and sixth terms is 44 and the sum of the first eighteen terms is thrice the sum of the first ten terms, find the value of the

a = 5.5, d = 11/3

Step-by-step explanation:

An arithmetic progression is a sequence of number such that the difference between consecutive numbers is a constant. It is given by:

The sum of fifth and sixth terms is 44

Therefore:

a + 4d + a + 5d = 44

2a + 9d = 44                       (1)

The sum of the first n terms is:

Since the sum of the first eighteen terms is thrice the sum of the first ten terms:

18a + 153d = 3(10a + 45d)

18 a + 153d = 30a + 135d

18a  - 30a + 153d - 135d = 0

-12a + 18d = 0                    (2)

Multiply equation 1 by 6 and add to equation 2:

72d = 264

d = 11/3

Putting d = 11/3 in eqn 2

-12a + 18(11/3) = 0

-12a + 66 = 0

12a = 66

a = 5.5

x + 107

step-by-step explanation:

let's say that the number he had before the mistake was x. then, he will have 107 dollars more than this, so the answer is x + 107.

the f

last graph i believe

step-by-step explanation:

worked it out i believe