Question

the first , second, and the nth terms of an arithmetic sequence are 2,6, and 58 respectively find the value of n

Answer 1

n = 15

the nth term of an arithmetic sequence is $a_{n}$ = a₁ + (n-1)d

where d is the common difference

d = a₂ - a₁ = 6 - 2 = 4

$a_{n}$ = 2 + 4n - 4 = 58

4n - 2 = 58

4n = 60 ( divide both sides by 4 )

n = 15