Determine the A.P., whose fifth term is 16 and the difference of the eighth term from the thirteenth term is 20.

Asked by 4321sandeep | 11th Oct, 2020, 11:46: AM

Expert Answer:

Question should be:
Determine the A.P., whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Solution:
Given: a5 = 19 i.e. a + 4d = 19 ... (i)
a13 - a8 = 20 i.e. a + 12d - a - 7d = 20 i.e. 5d = 20 
Therefore, d = 4
Substituting d in (i), we get
a + 4 x 4 = 19
a = 3
Hence, the required AP is 3, 7, 11, 15, 19, 23, 27, 31, ...
 
Note: If a5 = 16, we get a = 0 which contradict the statement a5 = 16

Answered by Renu Varma | 12th Oct, 2020, 10:14: AM