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The teacher's helper was putting cookies onto plates. He put $2$ cookies on the first plate, $4$ cookies on the second plate, $7$ cookies on the third plate, and $11$ cookies on the fourth plate. If this pattern continues, how many cookies will the helper put on the seventh plate?

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Sequences: word problems

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Q. The teacher's helper was putting cookies onto plates. He put

2

cookies on the first plate,

4

cookies on the second plate,

7

cookies on the third plate, and

11

cookies on the fourth plate. If this pattern continues, how many cookies will the helper put on the seventh plate?

Identify pattern in cookies: Step $1$ : Identify the pattern in the number of cookies on each plate. $\newline$ First plate: $2$ cookies, Second plate: $4$ cookies, Third plate: $7$ cookies, Fourth plate: $11$ cookies. $\newline$ We notice that the difference between the cookies on consecutive plates increases by $1$ each time. $\newline$ Difference between $1$ st and $2$ nd plate: $4 - 2 = 2$ $\newline$ Difference between $2$ nd and $3$ rd plate: $4$ $0$ $\newline$ Difference between $3$ rd and $4$ th plate: $4$ $3$
Continue pattern for more cookies: Step $2$ : Continue the pattern to find the number of cookies on the fifth, sixth, and seventh plates. $\newline$ Fifth plate: $11 + 5 = 16$ cookies $\newline$ Sixth plate: $16 + 6 = 22$ cookies $\newline$ Seventh plate: $22 + 7 = 29$ cookies

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