How do you find a general formula for each arithmetic sequence given 8th term is -20; 17th term is -47?

Feb 20, 2016

${n}^{t h}$ term of the arithmetic sequence is given by $4 - 3 n$

Explanation:

If $a$ is the first term of an arithmetic sequence and $d$ the difference between a term and its preceding term, general formula for ${n}^{t h}$ term of the arithmetic sequence is given by $a + \left(n - 1\right) d$.

As ${8}^{t h}$ term is $- 20$ and ${17}^{t} h$ term is $- 47$

$a + \left(8 - 1\right) d = a + 7 d = - 20$ and $a + \left(17 - 1\right) d = a + 16 d = - 47$.

Subtracting first equation from second, we get

$9 d = - 47 + 20$ or $9 d = - 27$ i.e. $d = - 3$

putting this in first we get $a + 7 \cdot \left(- 3\right) = - 20$ or $a = 1$.

Hence, ${n}^{t h}$ term of the arithmetic sequence is given by $1 - 3 \left(n - 1\right)$ or $4 - 3 n$