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For an AP whose fifth term is 19 and the difference between the eighth term from the thirteenth term is 20, then its 10th term is[[1]].

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Detailed Solution

For an AP whose fifth term is 19 and the difference between the eighth term and the thirteenth term is 20, then its 10th term is 39.
Given, 5th term = 19,
13th term - 8th term = 20.
Let the first term be

a

and the common difference be

d

.
Now, fifth term is,

a 5 = a + 5 − 1 d 19 = a + 4 d

Thirteenth term is,

a 13 = a + 13 − 1 d = a + 12 d

Eighth term is,

a_{8} = a + (8 - 1) d = a + 7 d

.
Putting values in the following,

a 13 − a 8 = 20 a + 12 d − a + 7 d = 20 a + 12 d − a − 7 d = 20 5 d = 20

d = 205 d = 4

Now, the value of

a

19 = a + 4 d a + 44 = 19 a + 16 = 19 a = 3

For 10th term,

a_{10} = 3 + (10 - 1) 4 = 39

.
Therefore, the final answer is 39.

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