Find the 20th term of the arithmetic progression 3,8,13,18,...

Expert Answers
justaguide eNotes educator| Certified Educator

The series 3, 8, 13, 18, ... is an arithmetic progression. In an AP the difference between two consecutive terms is constant. For the given series it is 18 - 13 = 13 - 8 = 8 - 3 = 5

The nth term of an AP is given by a + (n - 1)*d where the first term is a and the common difference is d.

We have a = 3 and the common difference d = 5

The 20th term is 3 + 19*5 = 3 + 95 = 98

The required term of the given AP is 98.

giorgiana1976 | Student

We notice that the difference between any two consecutive terms of the given a.p. is 5.

8-3 = 13-8 = 18-13 = 5

Therefore, the common difference of the given a.p. is d = 5. The first term of this a.p. is a1 = 3.

We'll recall the formula that gives any term of an arithmetical progression:

an = a1 + (n-1)*d

an is the nth term of the a.p.

We'll calculate a20 with this formula:

a20 = 3 + (20-1)*5

a20 = 3 + 19*5

a20 = 98

The 20th term of the given arithmetical progression is a20 = 98.