1條等差數列

a)
假設a 為首項, d 為公差,

2T(1)+3T(3)=39
2*(a) + 3*(a + 2d) = 39
5a + 6d = 39 (1)

3T(5)- T(2)=50
3*(a+4d) - (a+d) = 50
2a + 11d = 50 (2)

(1)*2 - (2)*5:
10a + 12d - 10a - 55d = 39*2 - 50*5
43d = 172
d = 4
把它代入 (1)式,
5a + 6*4 = 39
a = 3
所以首項是3, 公差是4.

b)
T(25) = a + 24d = 3 + 24*4
= 99.