Question

Zad znajdź wzór ciągu arytmetycznego jeśli:

a),

b),

c),

Answer 1

a)   a1 = 6r = 2

 

Jeśli (a_n) jest ciagiem arytmetycznym o różnicy r, to:

     a_n = a1 + (n-1) · r

dla dowolnego n ∈ N+

 

a1 = 2

6r = 2  /:6

r = ⅓

a_n = 2 + ⅓(n-1)

===============

 

b)  a3 = 7,  a6 = 16

 

a3 = a1+2r = 7

a6 = a1+5r = 16

 

a1+2r = 7

a1+5r = 16

--------------(-)

5r-2r = 16-7

3r = 9  /:3

r = 3 

a1 = 7-2r = 7-2·3 = 7-6

a1 = 1

 

a_n = 1 + 3(n-1)

==============

 

c)

a1 + a4 = 17

a2 + a8 = 32

 

a1 + a1 + 3r = 17

a1 + r + a1 + 7r = 32

 

2a1+3r = 17

2a1+8r = 32

---------------(-)

8r-3r = 32-17

5r = 15  /:5

r = 3

2a1 = 17-3r = 17-3·3 = 17-9 = 8

2a1 = 8  /:2

a1 = 4

 

a_n = 4 + 3(n-1)

==============