Question

por favor alguem me ajude...dada o 1 termo de uma P.A.a1:500 e sua razao r-2,determine

Answer 1

$S_n=\dfrac{(a_1+a_n)\cdot(n)}{2}$

$S_{45}=\dfrac{(a_1+a_{45})\cdot45}{2}$

$a_1=500$

$r=-2$

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

$a_{45}=500+44\cdot(-2)=500-88=412$

$S_{45}=\dfrac{(500+412)\cdot45}{2}=\dfrac{912\cdot45}{2}=456\cdot45=20~520$

Answer 2

$a_{45}=a_1+44.r\\ a_{45}=500+44*2\\ a_{45}=500+88\\ \\ a_{45}=588\\ \\ S_{45}=\frac{45(500+588)}{2}=\frac{45*1088}{2}=296.480$