Sorozat

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