find the h.p. whose 6th term is 1 and 10th term is 5. find 15th term of the series also.

Answer 1

so term(6) = 1/(a+5d) = 1
a+5d = 1 **

term(10) = 1/(a+9d) = 5
5a + 45d = 1 ***

** times 5 ---> 5a + 25d = 5
subtract from ***
20d = -4
d = -1/5
in **
a - 1 = 1
a = 2
so the HP is 1/2 , 5/9 5/8, 27/20, ...
term(15) = 1/(a+14d)
= 1/(2 - 14/5)
= -5/4