In The Arithmetic Sequence 3,7,11, Which Term Is 119?

In the arithmetic sequence 3,7,11, which term is 119?

 

Answer:

119 is the 30th term.

Step-by-step explanation:

Arithmetic sequence general rule:

an = a₁ + (n-1)(d)

Where:

an = last term  ⇒ 119

a₁ = first term  ⇒ 3

d = common difference  ⇒ (7-3 = 11 - 7) ⇒ 4

n = nth term in the sequence or the number of terms  ⇒  unknown

Find for what term is 119:

an = a₁ + (n-1)(d)

119 = 3 + (n-1)(4)

119 = 3 + 4n - 4

119 = -1 + 4n

4n = 119 + 1

4n/4 = 120/4

n = 30

119 is the 30th term in the given sequence 3, 7, 11, ..., 119.