Answer:
see explanation
Step-by-step explanation:
the n th term of an arithmetic sequence is
[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d
given [tex]t_{1}[/tex] = 3 and [tex]t_{2}[/tex] = 10, then
[tex]t_{2}[/tex] = 3 + d = 10 ⇒ d = 10 - 3 = 7
[tex]t_{n}[/tex] = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ]
= [tex]\frac{n}{2}[/tex][(2 × 3) + 7(n - 1) ]
= [tex]\frac{n}{2}[/tex](6 + 7n - 7 )
= [tex]\frac{n}{2}[/tex](7n - 1)
= [tex]\frac{7}{2}[/tex] n² - [tex]\frac{1}{2}[/tex] n
