Question

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

Answer 1

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

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
`a_(n)= a_(1)+(n-1)d`,

where
`a_(1)` is the first term, d is the constant difference and

n is the position of the term in the sequence

∵
`a_(1)=4`

∵ d = 3

∴
`a_(n)= 4+(n-1)3`

∴
`a_(n)= 4+3n-3`

∴
`a_(n)= 1+3n`

The segma notation is:

∑
`\left \ {{n=8} \atop {n=1}} \right.` (1 + 3n)

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