If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and 14th terms is - 3, then find the 10th term.
Let the first term and common difference of an AP are a and d, respectively.
Given
a3 + a8 = 7
As we know, nth term of an AP is
an = a + (n - 1)d
where a = first term
an is nth term
d is the common difference
a + 2d + a + 7d = 7
2a + 9d = 7
2a = 7 - 9d [ Eqn 1]
a7 + a14 = - 3
a + 6d + a + 13d = - 3
2a + 19d = - 3
7 - 9d + 19d = - 3 [ using eqn i]
7 + 10d = - 3
10d = - 10
d = - 1
using this value in eqn i
2a = 7 - 9 (- 1)
2a = 16
a = 8
Now,
a10 = a + 9d
= 8 + 9 (- 1)
= 8 - 9 = - 1