Question

# Find the $$12^{th}$$ term from the end of the A.P. : -2, -4, -6, ...., -100.

Solution

## Main concept used: To find the term from end, consider the given A.P. in reverse order and find the term. i.e., -100.... -6, -4, -2. Now, a = -100 $$d=a_{n+1}-a_n=-4-(-6)=-4+ 6=2$$$$\therefore n = 12$$ $$\Rightarrow a_n = a + (n - 1)d$$$$a_12 = -100 + (12 - 1) (2)$$$$= -100 + 11 \times 2 = -100 22$$ $$\Rightarrow a_{12} = -78$$ Hence, the 12th term from the last of A.P. -2, -4, -6, ...... -100 is -78. Maths

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