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dmitriy555 [2]
2 years ago
12

Each time Shelley goes tobthe store she likes to buy gum.She buys one pack for $1.00 and then another pack for $0.50 more.How mu

ch does she spend on the two packs in all?
please help??​
Mathematics
1 answer:
Umnica [9.8K]2 years ago
3 0

Answer:

$2.50

Step-by-step explanation:

Shelley buys one pack of gum for $1

Price of gum: $1

Total amount of money spent: $1.00

Shelley buys another pack of gum for $0.50 more

1 + 0.50 = 1.5

Price of gum: $1.50

Total amount of money spent: $2.50

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<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

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In the question,

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We need to find out the pattern for the recursive equation for the given conditions.

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We see that,

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Therefore, on checking, we observe that,

a_{n}=a_{n-1}+(n-1)^{2}

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0

which is true.

<u>At, </u>

<u>n = 2</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1

Which is also true.

<u>At, </u>

<u>n = 3</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5

Which is true.

<u>At, </u>

<u>n = 4</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

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