Question

Find the 87th term of the arithmetic sequence 1,14,27,….

Answer 1

Answer:

$a_{87}=1119$

Step-by-step explanation:

Arithmetic sequence:

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

where d is the common difference between terms and n is the index of any given term.

Find the difference between the terms in the given sequence here:

$14-1=13\\27-14=13$

Each term has a common difference of 13. Using that, you can write the equation for this sequence:

$a_n=1+(n-1)13$

Finally, you can use this equation to find the 87th term by plugging in 87 for n:

$a_{87}=1+(87-1)13\\a_{87}=1+(86)13\\a_{87}=1+1118\\a_{87}=1119$