Számtani sorozatok

A számtani sorozat meghatározása:

mindig ugyanannyival nő, vagy csökken (egyenletesen nő/csökken)

Jellemzők:
d = különbség
an = általános tag
Sn = első n-tag összege:

Képletek:

`an = a1 + (n - 1)·d`
`Sn = n·(a1 + an)/2`
`Sn = (2·a1 + (n-1)·d)·n/2`

Órai Feladatok:

1. a_3 = 10, a_5 = 6
d = ?, a1 =?, a10 = ?, S10 = ?

2. a_4 = 15, a_7 = 6
d = ?, a1 =?, a8= ?, S8 = ?

3. a_2 = 11, a_6 = -9
d = ?, a1 =?, a7 = ?, S7 = ?

4. a_5 = 12, a_7 = 9
d = ?, a1 =?, a10 = ?, S10 = ?

5. a_6 = 14, a_9 = 9
d = ?, a1 =?, a10 = ?, S10 = ?

Házi Feladatok:

1. a_4 = 8, a_6 = 4
d = ?, a1 =?, a9 = ?, S9 = ?

2. a_5 = 10, a_8 = 1
d = ?, a1 =?, a10 = ?, S10 = ?

3. a_3 = 22, a_7 = 2
d = ?, a1 =?, a8 = ?, S8 = ?

4. a_2 = 7, a_4 = 4
d = ?, a1 =?, a6 = ?, S6 = ?

5. a_6 = 8, a_9 = 3
d = ?, a1 =?, a10 = ?, S10 = ?