Find the sum of the first 20 terms of the AP 16+9+2+(-5)+....

Question

Create a graphic representation of an arithmetic progression (AP). Start with a long number line stretching from left to right. Mark the first point with a chunky red rectangular block signifying the number 16. To its right, place a slightly smaller yellow block for the number 9. Moving further right, use progressively smaller blocks to represent decreasing numbers down to the number -5. Represent the next unmarked terms with faded, smaller blocks to hint at the continuing sequence. The blocks should gradually decrease in size, to signify 20 terms in total. The image offers a crystal-clear illustration of the AP 16+9+2+(-5)+....

Find the sum of the first 20 terms of the AP 16+9+2+(-5)+....

Answer 1

a=16

d = -7
S20 = 20/2 (2*16 + 19(-7))

Answer 2

a=16

d=-7
S20=n/2[2a+(n-1)d]
S20=20/2[2*16+(20-1)-7]
S20=10[32-133]
S20=10(-101)
S20=-1010

Answer 3

Well, let's first find the common difference in this arithmetic progression. From the given pattern, it seems like each term decreases by 7. So, the common difference (d) is -7.

Now, we can use the formula to find the sum of the first n terms of an arithmetic progression:

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

In this case, the first term (a) is 16, and the common difference (d) is -7.

Putting all the values into the formula, we have:

S20 = (20/2)(2(16) + (20-1)(-7))

S20 = 10(32 + 19(-7))

S20 = 10(32 - 133)

S20 = 10(-101)

S20 = -1010

So, the sum of the first 20 terms of the given arithmetic progression is -1010. Now that's some negative humor!

Answer 4

To find the sum of the first 20 terms of an arithmetic progression (AP), we need to first identify the common difference (d) and the first term (a₁).

In this given AP, we can observe that each term is obtained by subtracting 7 from the previous term.

First term, a₁ = 16
Common difference, d = -7

Now we can use the formula for the sum of an Arithmetic Progression (Sₙ):

Sₙ = (n/2) * [2a₁ + (n-1)d]

where n is the number of terms.

Substituting the given values:
S20 = (20/2) * [2(16) + (20-1)(-7)]

Solving this equation step-by-step:

1. n/2 = 20/2 = 10
2. 2a₁ = 2(16) = 32
3. (n-1)d = (20-1)(-7) = 19(-7) = -133

S20 = 10 * [32 + (-133)]
S20 = 10 * (-101)
S20 = -1010

Therefore, the sum of the first 20 terms of the given AP is -1010.

Answer 5

To find the sum of the first 20 terms of the given arithmetic progression (AP), we can use the formula for the sum of an arithmetic series.

The formula to find the sum of an arithmetic series is:

Sn = (n/2)(a₁ + an),

where:
- Sn is the sum of the first n terms,
- n is the number of terms,
- a₁ is the first term, and
- an is the nth term.

First, let's determine the values of a₁ and the common difference (d).

In the given arithmetic progression, we can see that the first term (a₁) is 16, and the common difference (d) is obtained by subtracting the previous term from the current term. So, we have:

a₁ = 16
d = 9 - 16 = -7

Next, we need to find the value of the 20th term (an). To do this, we use the formula for finding the nth term of an arithmetic progression:

an = a₁ + (n - 1)d.

Substituting the values, we get:

a20 = 16 + (20 - 1)(-7)
= 16 + 19(-7)
= 16 - 133
= -117.

Now, let's substitute our known values into the formula for the sum of an arithmetic series:

S20 = (20/2)(a₁ + a20).

Substituting the values, we get:

S20 = (20/2)(16 + (-117))
= 10(-101)
= -1010.

Therefore, the sum of the first 20 terms of the given arithmetic progression is -1010.