#### Question

Find the n-th term and the first three terms of the arithmetic sequence having a_6= 5 and d = \dfrac{3}{2}

The n-th term of an arithmetic sequence is of the form

a_n = a_1 + (n – 1)d.

In this case,

a_6= 5 and d = \dfrac{3}{2}

Plug in the formula, we can find the value of the first term

a_6 = a_1 + (6 – 1)d.

a_1 = a_6-5d = 5-5\cdotp \dfrac{3}{2}=-\dfrac{5}{2}

a_2 = a_1+d = -\dfrac{5}{2} + \dfrac{3}{2} =-1

a_3=a_2+d = -1+ \dfrac{3}{2} =\dfrac{1}{2}

a_n=-\dfrac{5}{2}+(n-1)\dfrac{3}{2}

a_n = \dfrac{3}{2} n-4