Use sigma notation to represent the sum of the first eight terms of the following sequence: 4, 7, 10, … the summation from n equals 1 to 8 of negative 4 plus 3 times n the summation from n equals 1 to 8 of negative 1 plus 3 times n the summation from n equals 1 to 8 of 1 plus 3 times n the summation from n equals 1 to 8 of 4 plus 3 times n

" the summation from n equals 1 to 8 of 1 plus 3 times n " ⇒ 3rd answer

Step-by-step explanation:

The sequence is : 4 , 7 , 10 , ........

∵ 7 - 4 = 3

∵ 10 - 7 = 3

∴ The sequence is an arithmetic sequence, where the first term is 4

and the constant difference is 3

∵ The rule of the arithmetic sequence is ,

where is the first term, d is the constant difference and

n is the position of the term in the sequence

∵

∵ d = 3

∴

∴

∴

The segma notation is:

∑ (1 + 3n)

It means " the summation from n equals 1 to 8 of 1 plus 3 times n "

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.