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III.
Answer each problem. a, a₁ + (n-1)d
6. Joan started a new job with an annual salary of P150 000 in 2020. If she receives a
P12 000 raise each year, how much will her annual salary be in 2025?
7. A stack of telephone poles has 30 poles in the bottom row. There are 29 poles in the
second row, 28 in the next row, and so on. How many poles are there in the 26th row?
8. A gardener makes a triangular planting with 40 plants in the front row, 36 in the second row
32 in the third row, and so on. If the pattern is consistent, how many plants will there be in
the last row?
9. The second term of an arithmetic sequence is 24 and the fifth term is 3. Find the first term
and the common difference.
10. Find the 9th term of the arithmetic sequence with a₁ = 10 and d =
​

Sagot :

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Answer:

Let's solve each problem step by step:

Problem 6:

Joan's starting salary in 2020 = P150,000

Raise per year = P12,000

To find the salary in 2025, we need to calculate the total raise over the years and add it to the starting salary.

Starting from 2020 to 2025, there are 5 years.

Total raise = P12,000 * 5 years = P60,000

Annual salary in 2025 = Starting salary + Total raise

Annual salary in 2025 = P150,000 + P60,000 = P210,000

Therefore, Joan's annual salary in 2025 will be P210,000.

Problem 7:

This is an arithmetic sequence problem where the number of poles decreases by 1 in each row.

Given:

First row = 30 poles

Common difference (d) = -1 (decreasing by 1 each row)

n = 26 (row number to find)

The formula for the nth term of an arithmetic sequence is:

aₙ = a₁ + (n-1)d

Substitute the values:

aₙ = 30 + (26-1)(-1)

aₙ = 30 + 25(-1)

aₙ = 30 - 25

aₙ = 5

Therefore, there are 5 poles in the 26th row.

Problem 8:

This is also an arithmetic sequence problem.

Given:

First row = 40 plants

Common difference (d) = -4 (decreasing by 4 each row)

We need to find the number of plants in the last row, which is the nth term where n is the row number.

The formula for the nth term of an arithmetic sequence is:

aₙ = a₁ + (n-1)d

Since it's a decreasing pattern, the last row will have the first term.

Substitute the values:

aₙ = 40 + (n-1)(-4)

We need more information to determine the value of n or the number of plants in the last row.

Problem 9:

This problem involves finding the first term and the common difference of an arithmetic sequence given two terms.

Given:

Second term (a₂) = 24

Fifth term (a₅) = 3

We can form two equations using the arithmetic sequence formula:

a₂ = a₁ + d

a₅ = a₁ + 4d

Substitute the values:

24 = a₁ + d

3 = a₁ + 4d

Solve these two equations simultaneously to find the first term (a₁) and the common difference (d).

Problem 10:

To find the 9th term of an arithmetic sequence with a first term (a₁) of 10 and a common difference (d) missing, we need the value of the common difference (d) to calculate the 9th term using the arithmetic sequence formula:

aₙ = a₁ + (n-1)d

Please provide the missing value of the common difference (d) to proceed with finding the 9th term.

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