In the arithmetic sequence with 2n terms plus 1, the sum of all odd terms is 165, and the sum of all even terms is 150. Find the value of n, Teacher, I don't understand.

In the arithmetic sequence with 2n terms plus 1, the sum of all odd terms is 165, and the sum of all even terms is 150. Find the value of n, Teacher, I don't understand.


Mr. Dong is here
Odd items are n + 1 items, even items are n items
The median of the equivariance is a (n + 1)
The sum of odd terms is (n + 1) a (n + 1) = 165
The sum of even terms is Na (n + 1) = 150
The ratio is (n + 1) / N = 165 / 150
We get n = 10



In the arithmetic sequence with 2n + 1 terms, if the sum of all odd terms is 165 and the sum of all even terms is 150, then n is equal to ()
A. 9B. 10C. 11D. 12


From the odd number term and S1 = (n + 1) (a1 + A2N + 1) 2 = (n + 1) × 2An + 12 = (n + 1) an + 1 = 165, ① even number term and S2 = n (A2 + A2N) 2 = n × 2An + 12 = Nan + 1 = 150, ② n + 1n = 165150, the solution is n = 10



In the arithmetic sequence of 2n + 1, all odd number terms and 165, all even number terms 150, find n


According to an = a1 + (n-1) d
165 = sum of odd items
= a1+a3+..+a(2n+1)
= (n+1)(a1+nd) (1)
150 = sum of all even items
= a2+a4+..+a(2n)
= n(a1+nd) (2)
(1) (2) get
165/150 = (n+1)/n
11/10 =(n+1)/n
n =10