Arithmetic seq 2nd grade

What are the next terms in sequence -1 5 15 29 _ _?

Correct answer:

a5 =  47
a6 =  69

Step-by-step explanation:

a1=1 a2=5 a3=15 a4=29  d1=a2a1=5(1)=6 d2=a3a2=155=10 d3=a4a3=2915=14  Δ1=d2d1=106=4 Δ2=d3d2=1410=4 Δ1=Δ2=Δ3=  d4=d3+Δ1=14+4=18 d5=d4+Δ1=18+4=22  a5=a4+d4=29+18=47

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