Question 1

Question 1: If the 4th Term of an arithmetic sequence is 12, and the 7th term is 21, what is the first term and the common difference of the sequence?

Accepted Answer

a₁ = 3, d = 3

Answer

a₁ = 4, d = 3

Answer

a₁ = 5, d = 4

Question 2

Parallel 1.1

If the 5th term of an arithmetic sequence is $20$ and the 10th term is $50$ , find $a_1$

Accepted Answer

a₁ = -4,

d = 6

Answer

a₁ = -6,

d = 6

Answer

a₁ = -5,

d = -6

Question 3

Problem 2

If the 3rd term is $-2$ and the 8th term is $13$ , find $a_1$ and d.

Accepted Answer

a₁= -8

d = 3

Answer

a₁= -3

d = 9

Answer

a₁= -3

d = 8

Question 4

Parallel Question 1.3

If the 2nd term is $-2$ and the 5th term is $13$ , find $a_1$ and d.

(This one is a decreasing arithmetic sequence because the later term is smaller.)

Accepted Answer

a₁= 8

d = -1

Answer

a₁= 8

d = -2

Answer

a₁= 1

d = -8

Question 5

Question 2:

Given the arithmetic sequence: -6, 3, 12, 21, ...What is the 10th term of the sequence?

Accepted Answer

-28

Question 6

Parallel 2.1

If the sequence is $20$ Find: $a_1$

Accepted Answer

91

Question 7

Parallel 2.2

If the sequence is $20$ Find: $a_1$

Accepted Answer

-28

Question 8

Parallel 3

If the sequence is $20$ Find: $a_1$

Accepted Answer

38

Question 9

Question 3: While recovering from knee surgery, an athlete was advised by his trained to gradually return to his training routine. She recommended jogging for 12 minutes per session for the first week, with an additional 6 minutes per session for every week thereafter. In how many weeks will the athlete be jogging for 60 minutes per session?(Note: Numerical answers only)

Accepted Answer

9

Question 10

Parallel Question 3.1

A student practices piano for 20 minutes on the first day.Each day, she increases her practice time by 5 minutes.On which day will she practice for 65 minutes?

Accepted Answer

10

Question 11

Parallel Question 3.2

A gamer plays for 15 minutes on Day 1.He increases his playing time by 10 minutes each day.How many days until he plays 95 minutes?

Accepted Answer

9

Question 12

Parallel Question 3.3

A person practices drawing for 8 minutes on Week 1.Every week, they increase the practice time by 4 minutes.After how many weeks will they practice for 40 minutes?

Accepted Answer

9

Question 13

Question 4: A garden watering system costs P38 900.95. As time goes on, its value depreciate by PHP 4200.50 per year. Assuming that the annual depreciated amounts follow an arithmetic sequence, what is the value of the system after 4 years?

Accepted Answer

26299.45

Question 14

Parallel Question 4.1

A laptop is bought for ₱50,000.It depreciates by ₱6,000 per year.What is its value after 5 years?

Accepted Answer

26000

Question 15

Parallel Question 4.2

A car valued at ₱680,000 depreciates by ₱55,000 yearly.What is its value after 3 years?

Accepted Answer

570000

Question 16

Parallel Question 4.3

A mobile phone costs ₱24,500 and depreciates by ₱3,200 each year.Find its value after 6 years.

Accepted Answer

8500

Question 17

A university hired you as a laboratory assistant with a starting salary of P41 500 per month. Each year, you will receive a pay raise of P1700. How much will you earn at the start of your fifteenth year as a laboratory assistant?

Accepted Answer

65300

Question 18

Parallel Question 5.1

A teacher starts with a monthly salary of ₱32,000.Every year, she receives a raise of ₱1,200.How much will she earn at the start of her 10th year?

Accepted Answer

42800

Question 19

Parallel Question 5.2

A company hires an intern with a starting allowance of ₱18,500.He receives a yearly increase of ₱900.Find his allowance at the start of his 12th year.

Accepted Answer

28400

Question 20

Parallel Question 5.3

A research assistant starts with a salary of ₱27,750.Each year, the salary increases by ₱1,350.Find the salary at the start of the 20th year.

Accepted Answer

53400

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