a(n+1)=an+2 ; n is even = 2a(n-1) + 2 a(n+1) +2= 2(a(n-1) +2) [a(n+1) +2]/(a(n-1) +2) =2 [a(n+1) +2] / (a1+2) = 2^(n/2) a(n+1) +2 = 3.2^(n/2) a(n+1) = -2+3.2^(n/2) ; n is even n is even => n+1 is odd an = -2+ 3.2^[(n-1)/2] ; n is odd a1+a3+a5+.+a(2k-1)=3049 (-2+3.2^(0))+ (-2+3.2^(1)) +(-2+3.2^(2))+.+(-2+3.2^(k-1)) =3049 -2k + 3(2^k-1) =3049 k=10