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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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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's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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