Question

Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91

Answer 1

An arithmetic sequence, means that there is an equal difference between each number of the sequence. 

i.e. a, a+d, a+2d, a+3d...

where a is the first term, and d is the difference

in your case, a (first term) = 58

to find the difference, subtract 58 (a) from 69 (a+d) to get d. 

d = 69 - 58 = 11

(you can always check your calculation on another two consecutive terms: 91 - 80 also equals 11)

the general formula for any term in an arithmetic sequence is: 

T(n) = a + (n-1)d ...(or A(n))

in your case, n = 21

subbing into the formula: 

A21 = a + (21-1)d = 58 + 20(11) = 278

hope that helps :)