Question

Please Help! Asap!

Use sigma notation to represent the sum of the first six terms of the following sequence: −10, −13, −16, …

A) the summation from n equals one to 6 of quantity negative 10 plus 3 times n
B) the summation from n equals one to 6 of quantity negative 7 minus 10 times n
C) the summation from n equals one to 6 of quantity negative 7 minus 3 times n
D) the summation from n equals one to 6 of quantity negative 7 plus 3 times n

Answer 1

C

Explanation:

Answer 2

The Correct answer is C) the summation from n equals one to 6 of quantity negative 7 minus 3 times n

Explanation:

The given Arithmetic sequence: −10, −13, −16, …

Theory : For arithmetic sequence : a, a+d,a+2d......a+(n-1)d

Formula for summation is given as Sn =
`\sum\limits^(n=N)_(n=1) {a+(N-1)d}`

Where, a= First term of sequence = (-10) and d= difference of any two consecutive terms = (a+d)-(a) = (-13)-(-10)= (-3)

Putting values in Summation formula

Sn =
`\sum\limits^(n=N)_(n=1) {a+(N-1)d}`

Sn =
`\sum\limits^(n=6)_(n=1) {(-10)+(N-1)(-3)}`

Sn =
`\sum\limits^(n=6)_(n=1) {(-10) -3N+3)}`

Sn =
`\sum\limits^(n=6)_(n=1) {(-7-3N)}`

Thus, Correct answer is C) the summation from n equals one to 6 of quantity negative 7 minus 3 times n