Question

Encontre o décimo termo do seguinte P.A.
A)(1/2,1/4...)​

Answer 1

$> resolucao \\ \\ \geqslant progressao \: aritmetica \\ \\ > \: razao \: da \: pa \\ \\ r = a2 - a1 \\ r = \frac{1}{4} - \frac{1}{2} \\ r = \frac{1 - 2}{4} \\ r = - \frac{1}{4} \\ \\ = = = = = = = = = = = = = = = = = = = = = = = \\ \\ \geqslant \: o \: decimo \: termo \: da \: pa \\ \\ an = a1 + (n - 1)r \\ an = \frac{1}{2} + (10 - 1) - \frac{1}{4} \\ an = \frac{1}{2 } + 9 \times ( - \frac{1}{4} ) \\ an = \frac{1}{2} + ( - \frac{9}{4} ) \\ an = \frac{1}{2} - \frac{9}{4} \\ an = \frac{2 - 9}{4} \\ an = - \frac{7}{4} \\ \\ \\ > < > < > < > < > < > < > < > < > < > < > > >$

Answer 2

$\mathsf{a_n=a_1+\big(n-1\big)\cdot\underbrace{\sf\big( a_2-a_1\big)}_{\sf r}}$

$\mathsf{ a_{10}=\dfrac{1}{2}+\big(\sf10-1\big)\cdot\left(\sf\dfrac{1}{4}-\dfrac{1}{2}\right)}$

$\mathsf{ a_{10}=\dfrac{1}{2}+9\cdot\left(\sf-\dfrac{1}{4}\right)}$

$\mathsf{a_{10}=\dfrac{1}{2}-\dfrac{9}{4} }$

$\boxed{\boxed{ \mathsf{a_{10}=-\dfrac{7}{4}}} }$