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

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One of the most important question from ML Publication, Class10 Arithmetic Progression, Chapter 9 Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20

We know that, The first term of an AP = a And, the common difference = d. According to the question, 5th term, a5 = 19

Using the nth term formula, an = a + (n â€“ 1)d

We get, a + 4d = 19 a = 19 â€“ 4d â€¦(1) Also, 20th term â€“ 8th term = 20 a + 19d â€“ (a + 7d) = 20 12d = 20 d = 4/3 Substituting d = 4/3 in equation 1, We get, a = 19 â€“ 4(4/3) a = 41/3

Then, the AP becomes, 41/3, 41/3 + 4/3 , 41/3 + 2(4/3) 41/3, 15, 49/3

We know that, The first term of an AP = a And, the common difference = d. According to the question, 5th term, a5 = 19

Using the nth term formula, an = a + (n â€“ 1)d

We get, a + 4d = 19 a = 19 â€“ 4d â€¦(1) Also, 20th term â€“ 8th term = 20 a + 19d â€“ (a + 7d) = 20 12d = 20 d = 4/3 Substituting d = 4/3 in equation 1, We get, a = 19 â€“ 4(4/3) a = 41/3

Then, the AP becomes, 41/3, 41/3 + 4/3 , 41/3 + 2(4/3) 41/3, 15, 49/3