Question

26th , 11th and last term of an ap are zero, 3 and -1/5 respectively . find the common term and the number of terms.

Answer 1

t11 = 3
t26 = 0
tn = -1/5
consider t11 as a
so t26 is a16
an = a + (n-1)d
0 = 3 + 15d
-3 = 15d
-1 = 5d
d = -1/5
as t11 = 3
therefore to find a:
an = a + (n-1)d
3 = a + (10)(-1/5)
3 = a - 2
a = 5
an = a + (n-1)d
-1/5 = 5 + (n-1)(-1/5)
-5.2 = -n/5 + 1/5
-26 = 1-n
-27 = -n
n = 27
therefore the common difference is -1/5 and the number of terms is 27