Question

Fie (an)n>1 o progresie aritmetica. Stiind ca a4 + a15 = 46, sa se calculeze a7 + a12.

Answer 1

a₄  + a₁₅ = 46                      ( a₁ +3r) +( a₁ + 14r) = 46
2a₁ + 17r = 46 
atunci  a₇ + a₁₂ = ( a₁ + 6r) + ( a₁ + 11r)  = 2a₁ + 17r  = 46 

Answer 2

$\displaystyle a_4+a_{15}=46;~a_7+a_{12}=? \\ a_4+a_{15}=46 \\ a_{4-1}+r+ a_{15-1}+r=46 \\ a_3+r+a_{14}+r=46 \\ a_1+3r+a_1+14r=46 \\ 2a_1+17r=46 \\ a_7+a_{12}=a_{7-1}+r+a_{12-1}+r= a_6+r+a_{11}+r= \\ =a_1+6r+a_1+11r=2a_1+17r=46$