Find the next term in the sequence: 4, 7, 10, 13, .

Question

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Here are the solutions to the mathematics questions:

1. Find the next term in the sequence: 4, 7, 10, 13, ____

Find the common difference between consecutive terms.
$7 - 4 = 3$ $10 - 7 = 3$ $13 - 10 = 3$
The common difference is 3.
Add the common difference to the last term to find the next term.
$13 + 3 = 16$
The next term is 16.
The correct option is b) 16.

2. What is the nth term of the sequence 5, 8, 11, 14, ...?
Identify the first term ( $a$ ) and the common difference ( $d$ ).
The first term $a = 5$ .
The common difference $d = 8 - 5 = 3$ .
Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .
$T_n = 5 + (n-1)3$ $T_n = 5 + 3n - 3$ $T_n = 3n + 2$
The nth term is $*3n + 2*$ .
The correct option is a) $3n + 2$ .

3. What is the 10th term of the sequence with nth term $2n + 1$ ?
Substitute $n=10$ into the given nth term formula.
$T_n = 2n + 1$ $T_{10} = 2(10) + 1$
Calculate the value.
$T_{10} = 20 + 1$ $T_{10} = 21$
The 10th term is 21.
The correct option is c) 21.

4. Which of the following represents the sequence 6, 10, 14, 18, ...?
Identify the first term ( $a$ ) and the common difference ( $d$ ).
The first term $a = 6$ .
The common difference $d = 10 - 6 = 4$ .
Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .
$T_n = 6 + (n-1)4$ $T_n = 6 + 4n - 4$ $T_n = 4n + 2$
The sequence is represented by $*4n + 2*$ .
The correct option is a) $4n + 2$ .

5. A shirt costs N2,000. If its price increases by 10%, the new price is:
Calculate the amount of the increase.
$\text{Increase} = 10\% \text{ of N}2,000 = \frac{10}{100} \times 2000 = \text{N}200$
Add the increase to the original price.
$\text{New Price} = \text{N}2,000 + \text{N}200 = \text{N}2,200$
The new price is N2,200.
The correct option is b) N2,200.

6. A television costing N50,000 is reduced by 20%. Find the new price.
Calculate the amount of the reduction.
$\text{Reduction} = 20\% \text{ of N}50,000 = \frac{20}{100} \times 50000 = \text{N}10,000$
Subtract the reduction from the original price.
$\text{New Price} = \text{N}50,000 - \text{N}10,000 = \text{N}40,000$
The new price is N40,000.
The correct option is a) N40,000.

7. 25% of 240 is:
Calculate the percentage.
$25\% \text{ of } 240 = \frac{25}{100} \times 240$ $= \frac{1}{4} \times 240$ $= 60$
$25\%$ of 240 is 60.
The correct option is c) 60.

8. If a student's score increases from 60 to 72, the percentage increase is:
Calculate the absolute increase in score.
$\text{Increase} = 72 - 60 = 12$
Calculate the percentage increase using the formula $\frac{\text{Increase}}{\text{Original Score}} \times 100\%$ .
$\text{Percentage Increase} = \frac{12}{60} \times 100\%$ $= \frac{1}{5} \times 100\%$ $= 20\%$
The percentage increase is 20%.
The correct option is c) 20%.

9. A net is used to show the ____ of a solid.
A net is a two-dimensional pattern that can be folded to form a three-dimensional solid. It displays all the faces of the solid, which collectively form its surface.
The correct option is b) Surface.

10. Which solid has six square faces?
A cube is a three-dimensional solid object bounded by six identical square faces.
The correct option is c) cube.

Find the next term in the sequence: 4, 7, 10, 13, .

Answer

Step-by-step solution

Find the common difference between consecutive terms.

Add the common difference to the last term to find the next term.

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .

Substitute $n=10$ into the given nth term formula.

Calculate the value.

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .

Calculate the amount of the increase.

Add the increase to the original price.

Calculate the amount of the reduction.

Subtract the reduction from the original price.

Calculate the percentage.

Calculate the absolute increase in score.

Calculate the percentage increase using the formula $\frac{\text{Increase}}{\text{Original Score}} \times 100\%$ .

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More Mathematics Questions

Find the next term in the sequence: 4, 7, 10, 13, .

Answer

Step-by-step solution

Find the common difference between consecutive terms.

Add the common difference to the last term to find the next term.

Identify the first term (aaa) and the common difference (ddd).

Use the formula for the nth term of an arithmetic progression, Tn=a+(n−1)dT_n = a + (n-1)dTn​=a+(n−1)d.

Substitute n=10n=10n=10 into the given nth term formula.

Calculate the value.

Identify the first term (aaa) and the common difference (ddd).

Use the formula for the nth term of an arithmetic progression, Tn=a+(n−1)dT_n = a + (n-1)dTn​=a+(n−1)d.

Calculate the amount of the increase.

Add the increase to the original price.

Calculate the amount of the reduction.

Subtract the reduction from the original price.

Calculate the percentage.

Calculate the absolute increase in score.

Calculate the percentage increase using the formula IncreaseOriginal Score×100%\frac{\text{Increase}}{\text{Original Score}} \times 100\%Original ScoreIncrease​×100%.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .

Substitute $n=10$ into the given nth term formula.

Identify the first term ( $a$ ) and the common difference ( $d$ ).

Use the formula for the nth term of an arithmetic progression, $T_n = a + (n-1)d$ .

Calculate the percentage increase using the formula $\frac{\text{Increase}}{\text{Original Score}} \times 100\%$ .