Find the i. 10th term of 3, 7, 11, 15,... ii. 15th term of 10, 7, 4, 1,... iii. 20th term of 5, 10, 15…

Question

Find the i. 10th term of 3, 7, 11, 15,... ii. 15th term of 10, 7, 4, 1,... iii. 20th term of 5, 10, 15, 20,...

ScanSolve AI Tutor · Accepted Answer

These are arithmetic progressions. The formula for the n^(th) term of an arithmetic progression is T_n = a + (n−1)d, where a is the first term and d is the common difference. i) Find the 10^(th) term of 3, 7, 11, 15, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 3. The common difference is d = 7 − 3 = 4. Step 2: Use the formula for the n^(th) term with n=10. T₁₀ = a + (10−1)d; T₁₀ = 3 + (9)(4) Step 3: Calculate the 10^(th) term. T₁₀ = 3 + 36; T₁₀ = 39 The 10^(th) term is 39. ii) Find the 15^(th) term of 10, 7, 4, 1, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 10. The common difference is d = 7 − 10 = −3. Step 2: Use the formula for the n^(th) term with n=15. T₁₅ = a + (15−1)d; T₁₅ = 10 + (14)(−3) Step 3: Calculate the 15^(th) term. T₁₅ = 10 − 42; T₁₅ = −32 The 15^(th) term is −32. iii) Find the 20^(th) term of 5, 10, 15, 20, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 5. The common difference is d = 10 − 5 = 5. Step 2: Use the formula for the n^(th) term with n=20. T₂₀ = a + (20−1)d; T₂₀ = 5 + (19)(5) Step 3: Calculate the 20^(th) term. T₂₀ = 5 + 95; T₂₀ = 100 The 20^(th) term is 100.

Find the i. 10th term of 3, 7, 11, 15,... ii. 15th term of 10, 7, 4, 1,... iii. 20th term of 5, 10, 15, 20,...

Answers

Step-by-step solution

Part i· 3 steps

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

Use the formula for the $n^{th}$ term with $n=10$ .

Calculate the $10^{th}$ term.

Part ii· 3 steps
$\text{-32}$

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

Use the formula for the $n^{th}$ term with $n=15$ .

Calculate the $15^{th}$ term.

Part iii· 3 steps
$\text{100}$

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

Use the formula for the $n^{th}$ term with $n=20$ .

Calculate the $20^{th}$ term.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Find the i. 10th term of 3, 7, 11, 15,... ii. 15th term of 10, 7, 4, 1,... iii. 20th term of 5, 10, 15, 20,...

Answers

Step-by-step solution

Part i· 3 steps

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

Use the formula for the nthn^{th}nth term with n=10n=10n=10.

Calculate the 10th10^{th}10th term.

Part ii· 3 steps-32\text{-32}-32

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

Use the formula for the nthn^{th}nth term with n=15n=15n=15.

Calculate the 15th15^{th}15th term.

Part iii· 3 steps100\text{100}100

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

Use the formula for the nthn^{th}nth term with n=20n=20n=20.

Calculate the 20th20^{th}20th term.

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 $n^{th}$ term with $n=10$ .

Calculate the $10^{th}$ term.

Part ii· 3 steps
$\text{-32}$

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

Use the formula for the $n^{th}$ term with $n=15$ .

Calculate the $15^{th}$ term.

Part iii· 3 steps
$\text{100}$

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

Use the formula for the $n^{th}$ term with $n=20$ .

Calculate the $20^{th}$ term.