It is known that the sum of the first nine terms of the arithmetic sequence is 27, the sum of the first 29 terms is 290, and what is the sum of the first 19 terms?

S9=(a1+a9)*9/2=27,a1+a9=6
S29=(a1+29)*29/2=290,a1+a29=20
That is, 2a5 = a1 + A9 = 6, A5 = 3
2a15=a1+a29=20,a15=10
a1+a19=a5+a15=13
So S19 = (a1 + A19) * 19 / 2 = 13 * 19 / 2 = 247 / 2

Insert five numbers between 19 and 91 to form an arithmetic sequence. What is the arithmetic sequence?

There are seven items in this arithmetic sequence
19 is the first item
And because it is an arithmetic sequence, it has an = a1 + (n-1) d
91 = 19 + (7-1) * D can be obtained
D = 12
So according to the first term = 19, tolerance = 12, we can get the general term formula of arithmetic sequence: an = 12n + 7
These five numbers are 31, 43, 55, 67 and 79 respectively

What is the third-order arithmetic sequence? What is the meaning of the third-order arithmetic sequence? 1,3,6,11,19,31 why do you want to find the difference to explain the third-order arithmetic sequence

Meaning: a new sequence is obtained by subtracting two adjacent terms of a sequence, and then an arithmetic sequence is obtained, which is a three-level arithmetic sequence

3 + 6 + 9 + 99 equals ()

This is called the arithmetic function in senior high school, (first term + last term) * number of terms / 2 (3 + 99) * 33 / 2 = 1683

It is known that the sum of the first nine terms of the arithmetic sequence is 27, the sum of the first 29 terms is 290, and what is the sum of the first 19 terms?