Question

Determine a razao de uma pa em que a7=23 e a23=55

Answer 1

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

$a_7=a_1+6r \iff a_1+6r=23~~(i)$

$a_{23}=a_1+22r \iff a_1+22r=55~~(ii)$

Subtraindo $(ii)-(i)$:

$a_1+22r-a_1-6r=55-23$

$16r=32$

$r=\dfrac{32}{2}$

$r=2$