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


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