Question

Please help me with this Arithmetic Sequences and Series Question:

Identify the 37th term of the arithmetic sequence 2, 7, 12,…

Please show and explain all steps to get to the answer, thank you for your help and time.

Answer 1

The 37th term of arithmetic sequence is 182.

Step-by-step 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 37th term of arithmetic sequence :

`\implies{\sf{a_n = a_1 + \Big(n - 1\Big)d}}`

`\implies{\sf{a_(37) = 2 + \Big(37 - 1\Big)5}}`

`\implies{\sf{a_(37) = 2 + \Big( \: 36 \: \Big)5}}`

`\implies{\sf{a_(37) = 2 + 36 * 5}}`

`\implies{\sf{a_(37) = 2 + 180}}`

`\implies{\sf{a_(37) = 182}}`

`{\star{\underline{\boxed{\sf{\red{a_(37) = 182}}}}}}`

Hence, the 37th term of arithmetic sequence is 182.

`\rule{300}{2.5}`