Question

If for an A.P. s15 = 147 and s14= 123 find t15​

Answer 1

I assume
`t_n` denotes the n-th term of the sequence, and
`s_n` denotes the sum of the first n terms of the sequence. Then observe that

`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)`

so the 15th term in the sequence is 147 - 123 = 24.