Question

The first four terms of an arithmetic sequence are given.

Answer 1

Answer:

$a_6_0=322$

Step-by-step explanation:

we know that

The rule to calculate the an term in an arithmetic sequence is

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

where

d is the common difference

a_1 is the first term

we have that

$a_1=27\\a_2=32\\a_3=37\\a_4=42$

$a_2-a_1=32-27=5$

$a_3-a_2=37-32=5$

so

The common difference is d=5

$a_4-a_3=42-37=5$

Find  60th term of the sequence

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

we have

$a_1=27\\d=5\\n=60$

substitute

$a_6_0=27+5(60-1)$

$a_6_0=27+5(59)$

$a_6_0=322$