Find the 12th term from the end

Question:

Find the 12th term from the end of the AP – 2, – 4, – 6,……….,-100.

Solution:

Given AP -2, -4, -6,…,-100

Here, first term (a) = – 2, common difference (d) = – 4 – (-2) = -2 and the last term

(l) = -100.

We know,that, the nth term a„ of an AP from the end is a„ = l – (n – 1)d, where l is the last term and d is the common difference,

∴12th term from the end,

a12 =-100-(12-1)(-2)

= -100+ (11) (2) = – 100 + 22 = – 78.

Hence, the 12th term from the end is -78

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