Question

Find the 29th term 29,33,37,41
(arithmetic)

Answer 1

The 29th term of arithmetic sequence is 141.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

`\longrightarrow{\pmb{\sf{a_n = a_1 + (n - 1)d}}}`

• 
  `\pink\star` aₙ = nᵗʰ term in the sequence
• 
  `\pink\star` a₁ = first term in sequence
• 
  `\pink\star` n = number of terms
• 
  `\pink\star` d = common difference

Substituting all the given values in the formula to find the 29th term of arithmetic sequence :

• 
  `\purple\star` aₙ = a₂₉
• 
  `\purple\star` a₁ = 29
• 
  `\purple\star` n = 29
• 
  `\purple\star` d = 4

`\leadsto{\sf{ \: \: a_n = a_1 + (n - 1)d}}`

`\leadsto{\sf{ \: \: a_(29) = 29 + (29 - 1)4}}`

`\leadsto{\sf{ \: \: a_(29) = 29 + (28)4}}`

`\leadsto{\sf{ \: \: a_(29) = 29 + 28 * 4}}`

`\leadsto{\sf{ \: \: a_(29) = 29 + 112}}`

`\leadsto{\sf{ \: \: a_(29) = 141}}`

`\star \: \: \red{\underline{\boxed{\sf{a_(29) = 141}}}}`

Hence, the 29th term of arithmetic sequence is 141.

`\rule{300}{2.5}`

Answer 2

a₂₉ = 141

Explanation:

The nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 29 and d = a₂ - a₁ = 33 - 29 = 4 , then

a₂₉ = 29 + (28 × 4) = 29 + 112 = 141