Write an explicit formula that represents the sequence defined by the following recursive formula
1 answer:
Answer:
The explicit formula is a = 5 - 6n
Step-by-step explanation:
The explicit formula of the arithmetic sequence of the recursive formula
a = first term; a
= a
+ d is a
= a + (n - 1)d, where
- a is the first term
- d is the common difference between each two consecutive terms
- n is the position of the number
∵ The recursive formula is a = -1 and a
= a
- 6
→ Compare it with the formula above
∴ a = -1 ⇒ 1st term
∴ d = -6 ⇒ common difference
→ Substitute them in the form of the explicit formula
∵ a = -1 + (n - 1)(-6)
∴ a = -1 + (-6)(n) - (-6)(1)
∴ a = -1 + -6n - (-6)
∴ a = -1 - 6n + 6
→ Add the like term
∴ a = 5 - 6n
∴ The explicit formula is a = 5 - 6n
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Answer:
There are 650 cannonballs
Step-by-step explanation:
If you look closely in the picture, you can see that:
- 1st row has 1 ball
- 2nd row has 4 balls
- 3rd row has 9 balls
- 4th row has 16 balls
etc. etc.
We can see that the number of balls is the square of the row number. There are a total of 12 rows. So, rest of the rows has:
- 5th row has 25 balls
- 6th row has 36 balls
- 7th row has 49 balls
- 8th row has 64 balls
- 9th row has 81 balls
- 10th row has 100 balls
- 11th row has 121 balls
- 12th row has 144 balls
If we add up all those, we get total number of balls:
There are 650 cannonballs