Question

A1=5 a9=37 найти s12

Answer 1

A₁=5    a₉=37   S₁₂-?
a₉=a₁+8d=5+8d=37
8d=32  |÷8
d=4
a₁₂=a₁+11d=5+11*4=5+44=49
S₁₂=(a₁+a₁₂)*n/2=(5+49)*12/2=54*6=324.
Ответ: S₁₂=324.

Answer 2

To find the value of S12, we need to determine the pattern or rule that relates the given sequence A1=5, A9=37, and then use that rule to find the value of S12.

Let's examine the given sequence A1=5 and A9=37 to find the pattern:

A1 = 5 A9 = 37

We can observe that each term in the sequence is increasing, and the difference between consecutive terms is also increasing. Let's find the common difference (d) between consecutive terms:

d = A9 - A1 d = 37 - 5 d = 32

Now, we can find the general formula for the arithmetic sequence:

An = A1 + (n - 1) * d

where An is the nth term in the sequence and n is the term number.

Now, we can find S12, the sum of the first 12 terms of the sequence. The formula for the sum of an arithmetic sequence is:

Sn = n/2 * (A1 + An)

where Sn is the sum of the first n terms of the sequence.

We want to find S12, so n = 12:

S12 = 12/2 * (A1 + A12)

Now, we need to find A12 using the general formula for the arithmetic sequence:

A12 = A1 + (12 - 1) * d A12 = 5 + 11 * 32 A12 = 5 + 352 A12 = 357

Now, substitute the values back into the formula for S12:

S12 = 12/2 * (A1 + A12) S12 = 6 * (5 + 357) S12 = 6 * 362 S12 = 2172

Therefore, the value of S12 is 2172.