Question

An= S3=35 S10=120 a1-?

Answer 1

Можно подробнее обьяснить пож

Answer 2

To decipher the pattern in the given sequence, let's break down the problem:

The given sequence is: An= S3=35 S10=120

Here, "An" represents the nth term of the sequence, and "S3" and "S10" represent the sums of the first 3 terms and first 10 terms of the sequence, respectively.

We can find the common difference between consecutive terms using the formula for the sum of an arithmetic sequence:

Sum (Sn) = (n/2) * (a1 + an)

where "n" is the number of terms, "a1" is the first term, and "an" is the nth term.

Let's find the common difference (d):

S3 = 35 3/2 * (a1 + a3) = 35 (a1 + a3) = 70

S10 = 120 10/2 * (a1 + a10) = 120 5 * (a1 + a10) = 120 (a1 + a10) = 24

Now, we can set up two equations and solve for the first term (a1) and the common difference (d):

1. a1 + a3 = 70
2. a1 + a10 = 24

Subtracting equation 2 from equation 1:

(a1 + a3) - (a1 + a10) = 70 - 24 a3 - a10 = 46

Since we know that the common difference (d) is constant, we can write:

a3 - a10 = 2d

Substitute the known values:

46 = 2d

Now, solve for "d":

d = 46 / 2 d = 23

Now that we have the common difference (d), we can find the first term (a1) using equation 2:

a1 + a10 = 24

Substitute the known values:

a1 + (a1 + 9d) = 24 a1 + a1 + 9(23) = 24 2a1 + 207 = 24 2a1 = 24 - 207 2a1 = -183 a1 = -183 / 2 a1 = -91.5

Therefore, the first term (a1) is -91.5.

Now that we know the first term and the common difference, we can find the value of the first term (a1) of the sequence:

a1 = -91.5

The first term (a1) of the sequence is -91.5.