Question

write a(subscript)100th = 2(subscript)1 + (n-1)6 into a explict formula

Answer 1

To express the equation \( a_{100} = 2_1 + (n-1)6 \) in explicit form, we first need to clarify what the terms represent:

- \( a_n \) typically denotes the \( n \)-th term in a sequence.
- From your example, it looks like \( 2_1 \) might represent a constant (often written as \( a_1 \), which is the first term of the sequence).
- Let's replace \( 2_1 \) with \( a_1 = 2 \) for clarity in our calculations, given that the number \( 2 \) seems to derive from the first term.

The equation is then updated as follows:

\[
a_n = a_1 + (n-1)d
\]

Given \( a_1 = 2 \) and \( d = 6 \), we can substitute these values into the formula:

\[
a_n = 2 + (n-1)6
\]

Now, simplify the equation:

\[
a_n = 2 + 6(n-1)
\]
\[
a_n = 2 + 6n - 6
\]
\[
a_n = 6n - 4
\]

So, the explicit formula for the sequence is:

\[
a_n = 6n - 4
\]