How do you write a rule for the nth term of the arithmetic sequence and then find $a_10$ for $d=5, a_5=33$ ?

Question

1902 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-23T20:41:55

$a_n = 13 + 5*(n-1)$
$a_10 = 58$

The general form of $n^(th)$ term of an AP is given as:-

$a_n = a_1 + (n-1)*d$

In this case, $d = 5$
$therefore a_n = a_1 + 5*(n-1)$

$a_5 = a_1 + 5*(5-1) = a_1+5*4 = a_1 + 20$

But, $a_5 = 33$

$therefore 33 = a_1 +20$
$=> a_1 = 33-20 = 13$

Hence $a_n = 13 + 5*(n-1)$

$a_10 = 13 + 5*(10-1) = 13+5*9 = 13+45 = 58$

How do you write a rule for the nth term of the arithmetic sequence and then find a_10a_10 for d=5, a_5=33d=5, a_5=33?