If a1=5 and a5=15, how do you find the formula for the nth term of the sequence?

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Answer 1 · 2015-08-31T07:07:41

$color(blue)(a_n = 5+(n-1) *5/2)$

$a_1 = color(blue)(5$
$a_5=15$

The $nth$ term is denoted as:

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

So,
$a_5=a_1+(5-1)*d$

$15=5 +4d$

$15-5=4d$

$10=4d$

$d=10/4$

$color(blue)(d=5/2$

So the formula for $nth$ term can now be written as:
$a_n = a_1+(n-1)d$

$color(blue)(a_n = 5+(n-1) *5/2)$ where $(n =1,2,3...)$