Question

Determine if the following sequence is an Arithmetic Sequence. If it is, what would be the 31st term? NOTE: an=a1+(n-1)d

7, 11, 15....

A- 131
B- 127
C- 117

Answer 1

The arithmetic sequence of 31st term is 127.

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 31st term of arithmetic sequence :

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

`\leadsto{\sf{ \: \: a_(31) = 7+ (31- 1)4}}`

`\leadsto{\sf{ \: \: a_(31) = 7+ (30)4}}`

`\leadsto{\sf{ \: \: a_(31) = 7+ 30 * 4}}`

`\leadsto{\sf{ \: \: a_(31) = 7+ 120}}`

`\leadsto{\sf{ \: \: a_(31) =127}}`

`\star \: \: \pink{\underline{\boxed{\sf{\purple{a_(31) =127}}}}}`

Hence, the arithmetic sequence of 31st term is 127.

`\rule{300}{2.5}`