I assume [tex]t_n[/tex] denotes the n-th term of the sequence, and [tex]s_n[/tex] denotes the sum of the first n terms of the sequence. Then observe that
[tex]s_{15} - s_{14} = \displaystyle \sum_{n=1}^{15} t_n - \sum_{n=1}^{14} t_n \\\\ s_{15} - s_{14} = (t_1 + t_2 + \cdots + t_{14} + t_{15}) - (t_1 + t_2 + \cdots + t_{14}) \\\\ s_{15} - s_{14} = t_{15}[/tex]
so the 15th term in the sequence is 147 - 123 = 24.
