40 the first term of an arithmetic sequence is -12. the common difference of the sequence is 7. what is the sum of the first 30 terms of the sequence?

 2685

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Explanation:

When we want to add up the first n terms of an arithmetic sequence, the formula to use is

S = (n/2)*( 2*a+d(n-1) )

where

S = sum of the first n terms

n = number of terms

a = first term

d = common difference

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In this case,

S = unknown

n = 30

a = -12

d = 7

which means,

S = (n/2)*( 2*a + d*(n-1) )

S = (30/2)*( 2*(-12) + 7*(30-1) )

S = 15*(-24 + 7*29)

S = 15*(-24 + 203)

S = 15*(179)

S = 2685

This answer is confirmed using a spreadsheet. Basically I had the spreadsheet generate 30 terms based on a pattern I gave it of the first two terms. Then I used the "SUM" function to add up all 30 terms quickly getting 2685.

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Side note:

Another formula we could use is

S = (n/2)*(a_1 + a_n)

where

a_1 = first term

a_n = nth term, when n = 30 this is the 30th term

The a_n part is equal to a_n = a_1 + d(n-1), and when you add this to the a_1 already in the S formula, that accounts for the 2*a_1 back in the first formula mentioned at the top of the page.

sum of the first 30 terms is 2685

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 30 terms

a = - 12

d = 7

Therefore, the sum of the first 30 terms, S30 would be

S30 = 30/2[2 × - 12 + (30 - 1)7]

S30 = 15[- 24 + 203)

S30 = 15 × 179 = 2685

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.