Question

В геометрической прогрессии b1 = 54, q = 2/3. Найдите b4 и S4.

Answer 1

Ответ:

$b_1=54\ \ ,\ \ q=\dfrac{2}{3}\\\\\\b_4=b_1q^3=54\cdot \dfrac{8}{27}=2\cdot 8=16\\\\\\S_4=\dfrac{b_1(q^4-1)}{q-1}=\dfrac{54\cdot (\frac{16}{81}-1)}{\frac{2}{3}-1}=\dfrac{54\cdot (-\frac{65}{81})}{-\frac{1}{3}}=\dfrac{54\cdot 65}{27}=2\cdot 65=130$