Question

В геометрической прогрессии сумма первых пяти членов равна -242, b4/b1=27 и bn=-486. Чему равно n?

Answer 1

 

$<var>S_5 = b_1+b_2+b_3+b_4+b_5 = -242\\ \frac{b_4}{b_1} = 27\\ b_n = -486\\\\\\\\ 1) b_m = b_1*q^{m-1}\\\\ b_4 = b_1*q^{3}\\\\ q^3 = \frac{b_4}{b_1} = 27\\\\ q = 3\\\\\\\\ 2) S_m = \frac{b_1*(q^{m}-1)}{q-1}\\\\ S_5 = \frac{b_1*(3^{5}-1)}{3-1} = \frac{b_1*(243-1)}{2} = b_1*121 = -242\\\\ b_1 = -2\\\\\\\\\ 3) b_n = b_1*q^{n-1}\\\\ -486 = -2*3^{n-1}\\\\ 243 = 3^{n-1}\\\\ 3^{5} = 3^{n-1}\\\\ n = 6</var>$