Given that in A.P 4th term = 26 & 8th term = 72
= a + 3d = 26 and a + 7d = 72
∴ (a + 7d) - (a + 3d) = 72 - 26
= 4d = 46
= d = \(\frac {46}{4}\) = \(\frac {23}{2}\)
∴ a + 3 x \(\frac {23}{2}\)= 26
= a = 26 - \(\frac {69}{2} = \frac {52-69}{2} = \frac {-17}{2}\)
∴ 6th term = a+5d
= \( \frac {-17}{2} + 5\times \frac {23}{2}\)
= \( \frac {-17 + 115}{2} = \frac {98}{2} = 49\)
Hence, 6th term of A.P is 49
