Step: 1

[First time.]

Step: 2

Step: 3

Step: 4

Step: 5

[Observe the pattern.]

Step: 6

Step: 7

The recursive formula is a _{n} = a _{n - 1} + 10, n ≥2

Correct Answer is : a _{n} = a _{n - 1} + 10, n ≥2

Step: 1

[First time.]

Step: 2

Step: 3

Step: 4

[Observe the pattern.]

Step: 5

Step: 6

The explicit formula is a _{n} = 3n ^{2} + 5n , n ≥1

Correct Answer is : a _{n} = 3n ^{2} + 5n , n ≥1

Step: 1

[First term.]

Step: 2

Step: 3

Step: 4

Step: 5

[Observe the pattern.]

Step: 6

[Explicit formula.]

Step: 7

An explicit formula ia a _{n} = 2n + 10

Step: 8

[First time.]

Step: 9

Step: 10

Step: 11

Step: 12

[Observe the pattern.]

Step: 13

[Recursive formula.]

Step: 14

The recursive formula is a _{n} = a _{n - 1} + 2, n >2

Correct Answer is : a _{n} = 2n + 10, a _{n} = a _{n - 1} +2, n >2

Step: 1

[Pencils bought by 1st friend.]

Step: 2

[Pencils bought by 2nd friend.]

Step: 3

[Pencils bought by 3rd friend.]

Step: 4

[By observing the pattern.]

Step: 5

An explicit formula is a _{n} = n ^{3}

Step: 6

Step: 7

The number of pencils bought by Candy's 4^{th} friend are 64.

Correct Answer is : a _{n} = n ^{3}, 64

Step: 1

Step: 2

[First term.]

Step: 3

Step: 4

Step: 5

Step: 6

[Observe the pattern.]

Step: 7

Step: 8

Step: 9

[First term.]

Step: 10

Step: 11

Step: 12

Step: 13

[Observe the pattern.]

Step: 14

[Observe the pattern.]

Step: 15

An explicit formula ia a _{n} = 3n + 1

Step: 16

The recursive formula is a _{n} = a _{ n - 1} + 3, n≥2

Correct Answer is : a _{n} = 3n +1, a _{n} = a _{n - 1} +3, n ≥2

Step: 1

[Take No of employees at the age of 20 as first term.]

Step: 2

Step: 3

Step: 4

Step: 5

[Observe the pattern.]

Step: 6

Step: 7

The explicit formula is a_{n} = 4n

Step: 8

The number of employees at the age of 45 is a _{6} = 4(6) = 24

[Substitute the value.]

Correct Answer is : a _{n} = 4n , 24

Step: 1

[Take the number of students in the 1_{st} bus as first term.]

Step: 2

Step: 3

Step: 4

[Observe the sequence.]

Step: 5

[Observe the sequence.]

Step: 6

The recursive formula is a _{n} = a _{ n- 1} + 15, n≥2

Correct Answer is : a _{n} = a _{n - 1} + 15, n ≥2

Step: 1

[First term.]

Step: 2

Step: 3

Step: 4

[Observe the pattern.]

Step: 5

Step: 6

The explicit formula is a _{n} = 3n + 7

Correct Answer is : a _{n} = 3n + 7

Step: 1

[First term.]

Step: 2

Step: 3

Step: 4

[Observe the pattern.]

Step: 5

Step: 6

The explicit formula is a _{n} = 2n ^{2} + 3

Correct Answer is : a _{n} = 2n ^{2} + 3

Step: 1

[First term.]

Step: 2

Step: 3

Step: 4

[Observe the pattern.]

Step: 5

Step: 6

The recursive formula is a _{n} = 2a _{n -1} - 1, n ≥ 2

Correct Answer is : a _{n} = 2a _{n - 1} - 1, n ≥2

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