2,

Tekintsük egy sorozatnak, ahol

az első elem, ami osztható 7-tel, az 1001.

`a_1` = 1001

d = 7

Melyik lesz az utolsó elem?

1001+`(n-1)*7` < 2000

999 > (n-1)*7

n-1 < 142,71

n < 143,71

A sorozat 143. eleme lesz az utolsó elem.

`1001+7*(143-1)` = 1995

`a_(143)` = 1995

`S_(143)` = `((a_1+a_(143))*143)/2` = `((1001+1995)*143)/2` = 214 214 a keresett összeg.

1,

Számtani:

`a_1` = 16

`a_5` = `a_1` + 4d = 625

16 + 4d = 625

4d =

d = 152,25

`a_2` = `a_1` + d = 16 + 152,25 = 168,25

`a_3` = `a_2` + d = 168,25 + 152,25 = 320,5

`a_4` = `a_3` + d = 320,5 + 152,25 = 472,75



Mértani:

`a_1` = 16

`a_5` = 625 = `a_1*d^4`

`d^4` = `625/16` = 39,025

d = `pm` 2,5

Ha d = 2,5, akkor

`a_2` = `a_1*d` = `16*2.5` = 40

`a_3` = `a_2*d` = `40*2.5` = 100

`a_4` = `a_3*d` = `100*2.5` = 250

Ha d = -2,5, akkor

`a_2` = `a_1*d` = `16*-2.5` = -40

`a_3` = `a_2*d` = `-40*-2.5` = 100

`a_4` = `a_3*d` = `100*-2.5` =- 250

3, a,

`a_1` = 1

d = 1

`a_8` = `a_1+7*d` = 1 + `7*1` = 8

`S_8` = `(a_1+a_8)*8/2` = `(1+8)*8/2` = 36 elemű a torony

b,

`a_1` = 1

d = 2

`a_8` = `a_1+7*d` = `1+7*2` = 15

`S_8` = `(a_1+a_8)*8/2` = `(1+15)*8/2` = 64 elemű a torony.