The sum of the 1?? and the last term of an AP of 150 terms

Question

The sum of the 1st and the last term of an AP of 150 terms is equal to the sum of which of the following two terms?

Smart Achievers · Accepted Answer

(2)

For an AP of 150 terms, the sum of the 1?? term $t e r m a_{1} a n d t h e l a s t t e r m a_{150} i s$ equal to the sum of any two terms that are equidistant from the first and last term.

This means $a_{1} + a_{150} = a_{i} + a_{151 - i}$

Given the AP has 150 terms, the middle terms are $a ₇ ₅ a n d a ₇ ₆,$ which will have the same sum as $a ₁ a n d a_{150}$

Since $a_{75} + a_{76} = a_{1} + a_{150},$ we need to find two terms $a_{i} a n d a_{j}$ from the given options that satisfy

$a_{i} + a_{j} = a_{75} + a_{76}$

From the options, the correct pair is (i, j) = (20, 131), which satisfies

$a_{i} + a_{j} = a_{1} + a_{150}$

Solution

Q.
The sum of the 1st and the last term of an AP of 150 terms is equal to the sum of which of the following two terms

1 $15 ᵗ ʰ a n d 135 ᵗ ʰ$

2 $20 ᵗ ʰ a n d 131 ˢ ᵗ$

3 $50 ᵗ ʰ a n d 51 ˢ ᵗ$

4 $90 ᵗ ʰ a n d 60 ᵗ ʰ$

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Solution

Q. The sum of the 1st and the last term of an AP of 150 terms is equal to the sum of which of the following two terms

1 15ᵗʰ and 135ᵗʰ

2 20ᵗʰ and 131ˢᵗ

3 50ᵗʰ and 51ˢᵗ