Triangular apple trees problem. Please Help ASAP

[emma.20]

The Orchard brothers always plant their apple trees in triangular arrays. Each year they plant new trees (depicted in grey in the picture). This year they planted 31 new trees. If the orchard is still a triangle, how many apple trees are there in the orchard this year? Show all work.

 

[lev888]

The Orchard brothers always plant their apple trees in triangular arrays. Each year they plant new trees (depicted in grey in the picture). This year they planted 31 new trees. If the orchard is still a triangle, how many apple trees are there in the orchard this year? Show all work.
View attachment 24379

Are you studying arithmetic sequences? Do you see one here? What formula(s) do you think might be useful?

 

[Otis]

Hi emma. What is your class studying? Have you heard of the "triangular numbers"? There's a formula for those.

Also, have you noticed that the number of trees added each year is the same as the year number (i.e., 1 tree added in year 1, 2 trees added in year 2, 3 trees added in year 3, etc).

Please check out the forum's submission guidelines (here's a summary). We'd like to know what you've tried or thought about so far. Thanks!

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