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

Answer 1

Answer:

The arithmetic sequence of 31st term is 127.

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 :

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

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

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

$\leadsto{\sf{ \: \: a_{31} = 7+ 30 \times 4}}$

$\leadsto{\sf{ \: \: a_{31} = 7+ 120}}$

$\leadsto{\sf{ \: \: a_{31} =127}}$

$\star \: \: \pink{\underline{\boxed{\sf{\purple{a_{31} =127}}}}}$

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

$\rule{300}{2.5}$

Answer 2

Key points :-

᪥ The formula to find the 31st term is : $\sf \: a_{n} = a_{1} + (n - 1) \times d$

᪥ In the formula, $\sf \: a_{1}$ represents the first term of the sequence.

᪥ $\sf\:n$ is the number of terms, In our case n is 31.

᪥ $\sf\:d$ is the common difference between the terms, In our case d is 4.

$\green{ \rule{300pt}{3pt}}$

Detailed Solution is attached᭄