kazah
válasza
3 éve
1,
`a_1` = 8
d = -0.6
`a_(15)` = `a_1` + `14*d` = 8 + `14*(-0.6)` = -0,4
`S_(15)` = `(a_1+a_(15))*15/2` = `(8-0.4)*15/2` = 57
2,
`a_1` + `a_5` = 60 = `a_2` + `a_4` = `2*a_3`
`a_3` = 30
`S_5` = `a_1` + `a_2` + `a_3` + `a_4` + `a_5` = 60 + 60 + 30 = 150
3,
`a_1` = 12
`a_2` = a = `a_1` + d = 12+d
`a_3` = 6 = `a_1` + `2*d` = 12 + 2d
I. a = 12+d
II. 12 + 2d = 6
2d = -6
d = -3
a = 12 + (-3) = 9
4,
`a_1` = 52
d = 4
`a_n` = 500 = `a_1` + `(n-1)*d` = 52 + `(n-1)*4
`(n-1)*4` = 500-52 = 448
n-1 = `448/4 = 112
n = 113
`S_(113)` = `((a_1+a_(113))*113)/2` = `((52+500)*113)/2` = 31188
5,
`a_2` = 32
`a_6` = 2 = `a_2*q^4` = `32*q^4`
`q^4` = `1/16`
`q_1` = `1/2`
`q_2` = -`1/2`
6,
`a_1` = 5
q = 2
`S_8` = `a_1*(q^8-1)/(q-1)` = `5*(2^8-1)` = `5*255` = 1275
7,
`a_1` = 12
`a_3` = 75
`a_2` = `root()(a_1*a_3)` = `root()(12*75)` = `root()(900)` = `pm` 30
I. ha b = 30, akkor
30 = `a_1*q` = `12*q`
q = `30/12` = 2,5
II. ha b = -30, akkor
-30 = `12*q`
q = -2,5
8,
`a_1` = 500000 (ez a 0. év)
q = 1,025
`a_4` = `a_1*q^3` = `500000*1.025^3` = 538445 Ft
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