Summing $3+7+14+24+37...$ up to $10$ terms 
What is $3+7+14+24+37...$ up to $10$ terms? 

I only see that difference between two consecutive terms is in AP ie $7-3=4,14-7=7,24-14=10$ and so on. Any ideas on how to do it?

$x=1 \phantom{n} 2 \phantom{n}  3 \phantom{n}  4$
$y=3 \phantom{n}  7 \phantom{n} 14 \phantom{n} 24$
$y=m_2(x-x_1)(x-x_2)+m_1(x-x_1)+y_1$
$m_1$ is slope 
$m_1=(y_2-y_1)/(x_2-x_1)$
$m_1=(7-3)/(2-1)$
$m_1=4$
$m_2$ changes in slope 
$m_2=((y_3-y_2)-(y_2-y_1))/(x_3-x_1)$
$m_2=((14-7)-(7-3))/(3-1)$
$m_2=3/2$
$y=3/2*(x-2)(x-1)+2*(x-1)+3$ 
$y=1.5x^2-0.5x+4$
