Question

Дано bn прогресія q=1/5 s4=156 знайти: b1

Answer 1

$S_n= \frac{b_1(1-q^n)}{1-q} \\ S_4= \frac{b_1(1-( \frac{1}{5} )^4)}{1-\frac{1}{5}}=\frac{b_1(1- \frac{1}{5^4} )}{\frac{4}{5}} =\frac{b_1(5- \frac{1}{5^3} )}{4}=\frac{b_1(5- \frac{1}{125} )}{4}=\frac{b_1(\frac{625-1}{125} )}{4}= \\ \frac{b_1(\frac{624}{125} )}{4}=b_1 \frac{156}{125}$

$b_1 \frac{156}{125} =156$

b₁=125

Answer 2

$1) 156= \frac{ b_{1}*( 0.2 ^{4} -1)}{1-0.2}$
$2) 156= \frac{ -0.9984*b_{1}}{0.8}$
$3) -1.248*b_{1}=156$
$b_{1}= \frac{156}{-1.248}=-125$