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

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

Uniteasy Admin · Accepted Answer

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
$$a_6 = a_1 + (6 – 1)d.$$
$$a_1 = a_6-5d = 5-5\cdotp \dfrac{3}{2}=-\dfrac{5}{2} $$
$$a_2 = a_1+d = -\dfrac{5}{2} + \dfrac{3}{2} =-1$$
$$a_3=a_2+d = -1+ \dfrac{3}{2} =\dfrac{1}{2} $$
$$a_n=-\dfrac{5}{2}+(n-1)\dfrac{3}{2} $$
$$a_n = \dfrac{3}{2} n-4$$

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