1) b4=b1•q^3
b2=b1•q
b3=b1•q^2
{b1•q^3–b1•q=30
{b1•q^3–b1•q^2=24
{b1•q(q^2–1)=30
{b1•q^2(q–1)=24
{b1•q(q–1)(q+1)=30
{b1•q^2(q–1)=24
Разделим первое на второе:
q+1 5
----- = ---
q 4
4(q+1)=5q
4q+4=5q
q=4
b1=30/q(q^2–1)=30/60=1/2
Ответ: b1=1/2; q=4
2) b2=b1•q
b5=b1•q^4
b3=b1•q^2
b4=b1•q^3
{b1•q–b1•q^4=78
{b1•q^2+b1•q^3+b1•q^4=–117
{b1•q(1–q^3)=78
{b1•q^2(1+q+q^2)=–117
Разделим первое на второе:
1–q^3 2
--------------- = – ----
q(1+q+q^2) 3
(1–q)(1+q+q^2) 2
-------------------- = – ----
q(1+q+q^2) 3
1–q 2
----- = – ----
q 3
3–3q = –2q
q=3
b1=78/q(1–q^3)=78/3•26=78/78=1
Ответ: b1=1; q=3