State true or false.

If the first and last terms of an AP are a and $l$ respectively, then the sum of the nth term from the beginning and the nth term from the end is $a + l$ .

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False

True

answer is A.

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Detailed Solution

Given that the first and last terms of an AP are a and

l

.
The formula for the nth term from starting is,

a n = a + n − 1 × d

. ……(1)
The formula which gives the nth term of an AP from the end is,

a n = l − (n − 1) d

. ……(2)
By adding equations (1) and (2),

= a + (n − 1) d + {l − (n − 1) d} = a + (n − 1) d + l − (n − 1) d = a + l

Hence, the sum of the nth term from the beginning and the nth term from the end is a + 1.
Hence the statement is true.
Hence option 1 is correct.

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