Question

Let $a_1, a_2, a_3,\dots$ be an arithmetic sequence. if $a_{23} = \dfrac23$ and $a_{53} = \dfrac32$, what is $a_{35}$?

Answer 1

Using an arithmetic sequence, it is found that the 35th value of the sequence is given by: $a_{35} = 1$.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n - 1)d$

In which $a_1$ is the first term.

Considering that we have the mth term as reference, the nth term is also given as follows:

$a_n = a_m + (n - m)d$

In this problem, we have that:

$a_{23} = \frac{2}{3}, a_{53} = \frac{3}{2}$.

Hence:

$a_n = a_m + (n - m)d$

$a_{53} = a_{23} + (53 - 23)d$

$30d = \frac{3}{2} - \frac{2}{3}$

$30d = \frac{9 - 4}{6}$

$30d = \frac{5}{6}$

$d = \frac{1}{36}$

Then the 35th term is:

$a_{35} = a_{23} + 12d = \frac{2}{3} + 12\frac{1}{36} = \frac{2}{3} + \frac{1}{3} = 1$

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

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