Answer:
see explanation
Step-by-step explanation:
the nth term (explicit formula) of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + d(n - 1)
a₁ is the first term, d the common difference, n the term number
(9)
given a₁ = 1 and d = [tex]\frac{1}{2}[/tex] , then the explicit formula is
[tex]a_{n}[/tex] = 1 + [tex]\frac{1}{2}[/tex] (n - 1) = 1 + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + [tex]\frac{1}{2}[/tex]
use this formula to calculate a₅₂
a₅₂ = [tex]\frac{1}{2}[/tex] × 52 + [tex]\frac{1}{2}[/tex] = 26 + [tex]\frac{1}{2}[/tex] = 26 [tex]\frac{1}{2}[/tex]
(10)
given a₁ = 3 and d = [tex]\frac{3}{2}[/tex], then the explicit formula is
[tex]a_{n}[/tex] = 3 + [tex]\frac{3}{2}[/tex] (n - 1) = 3 + [tex]\frac{3}{2}[/tex] n - [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{2}[/tex] n + [tex]\frac{3}{2}[/tex]
use this formula to calculate a₅₂
a₅₂ = [tex]\frac{3}{2}[/tex] × 52 + [tex]\frac{3}{2}[/tex] = 78 + 1 [tex]\frac{1}{2}[/tex] = 79 [tex]\frac{1}{2}[/tex]
