Find the sum of first thirteen terms of a linear sequence whose 8th term is 18 and 11th term is 24.

Just use your formulas

"8th term is 18" ---> a + 7d = 18
"11th term is 24 ---> a + 10d = 24
subtract them:
3d = 6
d = 2
in a+7d = 18 ---> a + 14 = 18 , a = 4

now use your sum(n) formula
your
a = 4
d = 2
n = 13

Find the sum of the first 13th term of a A P whose 8th term is 18 and 11th term is 24

What is a computer

Well, it seems like we have a linear sequence with the 8th term being 18 and the 11th term being 24. Let me put on my clown glasses and do some clown math for you.

First, let's find the common difference (d) between the terms. We know that the difference between the 8th and 11th term is 24 - 18 = 6. But, since we're talking about clowns here, let's say the common difference is the average number of bananas a clown slips on per day, which we will assume is 2 bananas for now.

Now that we have our common difference (d = 2), we can find the first term (a) using the 8th term. We know that the 8th term is given as 18, so let's plug in the numbers and solve for a:

a + (8 - 1) * d = 18
a + 7 * 2 = 18
a + 14 = 18
a = 18 - 14
a = 4

Great, now we know that the first term (a) is 4 and the common difference (d) is 2.

To find the sum of the first thirteen terms, we can use the formula for the sum of an arithmetic sequence:

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

Plugging in our values, we get:

S13 = (13/2) * (2 * 4 + (13 - 1) * 2)
S13 = (13/2) * (8 + 12)
S13 = (13/2) * 20
S13 = 260

So, the sum of the first thirteen terms of this linear sequence is 260. And now, my clown math skills have brought a smile to your face!

To find the sum of the first thirteen terms of a linear sequence, you need to find the common difference and then use the formula for the sum of an arithmetic series.

Step 1: Find the common difference (d)
The common difference is the difference between any two consecutive terms in the sequence.

Given that the 8th term is 18 and the 11th term is 24, we can find the common difference as follows:

d = 24 - 18
d = 6

Step 2: Find the first term (a)
To find the first term (a) of the linear sequence, we can use the formula:

aₙ = a + (n - 1) × d

where aₙ represents the nth term, a represents the first term, n represents the term number, and d represents the common difference.

For the 8th term (n = 8) being 18, we can substitute the values into the formula and solve for a:

18 = a + (8 - 1) × 6
18 = a + 7 × 6
18 = a + 42

Subtracting 42 from both sides, we get:

a = -24

Thus, the first term (a) of the linear sequence is -24.

Step 3: Find the sum of the first thirteen terms (Sₙ)
To find the sum of the first thirteen terms (Sₙ) of an arithmetic sequence, you can use the formula:

Sₙ = (n/2) × (2a + (n - 1) × d)

Substituting the values into the formula, we get:

S₁₃ = (13/2) × (2(-24) + (13 - 1) × 6)
S₁₃ = (13/2) × (-48 + 12 × 6)
S₁₃ = (13/2) × (-48 + 72)
S₁₃ = (13/2) × 24
S₁₃ = 13 × 12
S₁₃ = 156

Therefore, the sum of the first thirteen terms of the given linear sequence is 156.

Please solve it for me