How to find the first term and common difference in AP?

Question

Given that $a_1,a_2,\dots$ is an arithmetic sequence. Let $a_3=-2$, $a_{21}=70$.

Find the first term $a_1$ and common difference $d$.

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The $n$th term of arithmetic sequence is $$a_n=a_1+d(n-1).$$

Using the above formula how to find $a_1$ and $d$?

Answer 1

Though SE expects your effort, I give hint so that you can give your $50\%$ effort.

Hint:

Given $$a_3 = a_1 + (3-1) d = -2 \tag{1}$$ and $$a_{21} = a_1 + (21-1) d = 70 \tag{2}$$.

So solving these two equation with two unknown $a_1$ and $d$, leads to answer??