Răspuns:
[tex]\boldsymbol{ \red{ a_{15} = 24}}[/tex]
Explicație pas cu pas:
[tex]S_{k} = \dfrac{(a_{1} + a_{k}) \cdot k}{2} = \dfrac{[a_{1} + a_{1} + (k - 1) \cdot r] \cdot k}{2}\\[/tex]
[tex]\dfrac{[-4 - 4 + (k - 1) \cdot 2] \cdot k}{2} = 150 \Rightarrow (-4 + k - 1) \cdot k = 150\\[/tex]
[tex](k - 5) \cdot k = 150 \Rightarrow k^2 - 5k - 150 = 0\\[/tex]
(k + 10)(k - 15) = 0
k ∈ N ⇒ k = 15
a₁₅ = a₁ + 14r = -4 + 14·2
a₁₅ = 24
Formula este:
[tex]\boxed{\boldsymbol{S_{n} = \dfrac{(a_{1} + a_{n}) \cdot n}{2} }}[/tex]
