Question

calcule a soma dos 11 primeiros termos de uma pg (1/4,1/2, 1,2,4..)

Answer 1

Olá!!

 

$<var>a1=\frac {1} {4}\\ \\ q=\frac {1} {2} : \frac {1} {4}-->\frac {1.4} {2.1}=\frac {4} {2}-->(2)\\ \\ n=11\\ \\ Sn=?\\ \\ --------------------\\ \\ Sn=\frac {a1.(q^n-1)} {q-1}\\ \\ S7=\frac {1/4.(2^1^1-1)} {2-1}\\ \\ S7=\frac {1/4.(2048-1)} {1}\\ \\ S7=\frac {1} {4}.2047\\ \\ S7=\frac {2047} {4}</var>$

Answer 2

Observe que:

 

$\text{S}_{\text{n}}=\dfrac{\text{a}_1\cdot(\text{q}^{\text{n}}-1)}{\text{q}-1}$

 

Note que:

 

$\text{q}=\dfrac{\text{a}_2}{\text{a}_1}=\dfrac{\frac{1}{2}}{\frac{1}{4}}=\dfrac{1}{2}\cdot\dfrac{4}{1}=2$

 

Logo:

 

$\text{S}_{11}=\dfrac{\frac{1}{4}\cdot(2^{11}-1)}{2-1}=\dfrac{\frac{1}{4}\cdot2~047}{1}=\dfrac{2~047}{4}$

 

Portanto, a soma dos 11 primeiros termos da P.G. (1/4, 1/2, 1, 2, 4, ...) é $\dfrac{2~047}{4}$.