Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20

Solution:

First term of an AP = a

Common difference = d

From the question,

5th term, a5 = 19

By using the nth term formula,

an = a + (n - 1)d

Substituting the values

a + 4d = 19

a = 19 - 4d …(1)

Here,

13th term - 8th term = 20

a + 12d - (a + 7d) = 20

5d = 20

d = 4

Now substitute d value in equation 1,

a = 19 - 4(4)

a = 3

So the AP is,

3, 3 + 4 , 3 + 2(4),…

3, 7, 11,…

Therefore, the AP is 3, 7, 11, ……

✦ Try This: Determine the AP whose fourth term is 13 and the difference of the sixth term from the fifteenth term is 18

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 5

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20

Summary:

The AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20 is 3, 7, 11, ……

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☛ Related Questions:

• The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP
• Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12
• If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term