Question

Em uma PA, seja 1 e 29 o primeiro e o quinto termo. Calcule a soma dos seis primeiros termos dessa PA


Na PG (1/4, x, 4, y),qual o valor de y - x? *

Answer 1

$\large\boxed{\begin{array}{l}\sf 1)\\\rm a_1=1~~a_5=29\\\rm a_5=a_1+4r\\\rm 29=1+4r\\\rm 4r=29-1\\\rm 4r=28\\\rm r=\dfrac{28}{4}\\\\\rm r=7\\\rm a_6=a_5+r\\\rm a_6=29+7=36\\\rm S_6=\dfrac{\backslash\!\!\!6\cdot(36+1)}{\backslash\!\!\!2}\\\\\rm S_6=3\cdot37\\\rm S_6=111\end{array}}$

$\large\boxed{\begin{array}{l}\sf 2)\\\rm \bigg(\dfrac{1}{4},x,4,y\bigg)\\\rm a_1=\dfrac{1}{4}=2^{-2}\\\\\rm a_3=4=2^2\\\rm a_3=a_1\cdot q^2\\\rm 2^2=2^{-2}\cdot q^2\\\rm q^2=\dfrac{2^2}{2^{-2}}\\\rm q^2=2^{2+2}\\\rm q^2=2^4\\\rm q=\sqrt{2^4}\\\rm q=2^2=4\\\rm x=\dfrac{1}{4}\cdot4=1\\\rm y=4\cdot4=16\\\rm y-x=16-1\\\huge\boxed{\boxed{\boxed{\boxed{\rm y-x=15}}}}\end{array}}$