In the known arithmetic sequence {an}, the 10th term is 23 and the 25th term is - 22, (1) Find S10 (2) find the maximum value of Sn

In the known arithmetic sequence {an}, the 10th term is 23 and the 25th term is - 22, (1) Find S10 (2) find the maximum value of Sn

（1）a10=a1+9d=23a25=a1+24d=-2215d=-45d=-3a1=23-9*(-3)=23+27=50S10=10a1+10*9/2*d=500+45*(-3)=500-135=365(2)Sn=na1+n (n-1)d/2=50n+n(n-1)(-3/2)=-3/2n^2+103/2n=n(-3/2n+103/2)n=17Smax=442

Let the 10th term of the arithmetic sequence be 23 and the 25th term be - 22. Find the general term formula an of the arithmetic sequence {an} and point out that it is less than 0 from which term

a10=23
a25=-22
a25-a10=a1+24d-a1-9d=15d=-22-23
d=-3
a10=a1+9d=a1-27=23
a1=50
an=50-3(n-1)=-3n+53
an

The following question: "known arithmetic sequence large (a), the fourth item is 10, the eighth item is 22, find the 10th item" find the answer

a4=10
a8=22
d=(22-10)÷4=3
therefore
a10=a8+2d=22+6=28
The tenth is 28