Написать формулу общего члена геометрической прогрессии, в которой:
1) a1 = 7, a2 = 8; 4) a1 = sin φ, a2 = 1/2 sin φ;
2) a1 = 3, a4 = 1/3; 5) a1 = tg φ, a2 = 1
3) a3 = a5 = —1; 6) a1 = cos φ, a2 = ctg
1) a1 = 7, a2 = 8; 4) a1 = sin φ, a2 = 1/2 sin φ;
2) a1 = 3, a4 = 1/3; 5) a1 = tg φ, a2 = 1
3) a3 = a5 = —1; 6) a1 = cos φ, a2 = ctg
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1) a1=7, a2=8, q=8/7,a(n)=a1*q^(n-1)=7*(8/7)^(n-1)=(49/8)*(8/7)^n;
2) a1=3, a4=1/3, 1/3=3*q^3, q^3=1/3:3=1/9, q=
3) a1=-1, a5=-1, -1=-1*q^4, q^4=1, q=1 или q=-1,
a(n)=a1*q^(n-1)=(-1)*1^(n-1)=-1^n или a(n)=(-1)*(-1)^(n-1)=(-1)^n;
4) a1=sinα, a2=1/2sinα, q=1/2sinα : sinα=1/2,
a(n)=a1*q^(n-1)=sinα*(1/2)^(n-1)=2sinα*(1/2)^n;
5) a1=tgα, a2=1, q=1/tgα,
a(n)=a1*q^(n-1)=tgα*(1/tgα)^(n-1)=tg²α*(1/tgα)^n;
6) a1=cosα, a2=ctgα, q=ctgα/cosα=1/cosα.
a(n)=a1*q^(n-1)=cosα*(1/cosα)^(n-1)=cos²α*(1/cosα)^n.