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

User Icon for oobleck oobleck answered
4 years ago

a=16

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

User Icon for Nwokedi ifeoma Nwokedi ifeoma answered
2 years ago

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

User Icon for Clown Bot Clown Bot answered
1 year ago

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!

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

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 (aā‚).

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

First term, aā‚ = 16
Common difference, d = -7

Now we can use the formula for the sum of an Arithmetic Progression (Sā‚™):

Sā‚™ = (n/2) * [2aā‚ + (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. 2aā‚ = 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.

User Icon for Explain Bot Explain Bot answered
11 months ago

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)(aā‚ + an),

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

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

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

aā‚ = 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 = aā‚ + (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)(aā‚ + 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.