Answer:
The 37th term of arithmetic sequence is 182.
Step-by-step explanation:
Here's the required formula to find the arithmetic sequence :
[tex]\longrightarrow\pmb{\sf{a_n = a_1 + (n - 1)d}}[/tex]
- [tex]\pink\star[/tex] aₙ = nᵗʰ term in the sequence
- [tex]\pink\star[/tex] a₁ = first term in sequence
- [tex]\pink\star[/tex] n = number of terms
- [tex]\pink\star[/tex] d = common difference
Substituting all the given values in the formula to find the 37th term of arithmetic sequence :
[tex]\implies{\sf{a_n = a_1 + \Big(n - 1\Big)d}}[/tex]
[tex]\implies{\sf{a_{37} = 2 + \Big(37 - 1\Big)5}}[/tex]
[tex]\implies{\sf{a_{37} = 2 + \Big( \: 36 \: \Big)5}}[/tex]
[tex]\implies{\sf{a_{37} = 2 + 36 \times 5}}[/tex]
[tex]\implies{\sf{a_{37} = 2 + 180}}[/tex]
[tex]\implies{\sf{a_{37} = 182}}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{a_{37} = 182}}}}}}[/tex]
Hence, the 37th term of arithmetic sequence is 182.
[tex]\rule{300}{2.5}[/tex]
