Answer the questions based on the given information. Numbers are written on the Chess Board as given
If $a_{8} = a_{1} + a_{2} + a_{3} + . . . . . . . + a_{7}$
$b_{8} = b_{1} + b_{2} + b_{3} + . . . . . . + b_{7}$
.................
..................
$h_{8} = h_{1} + h_{2} + h_{3} + . . . . . + h_{8} =$
What is $a_{8} + b_{8} + . . . . + h_{8} =$

2080

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1596

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399

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741

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Solution

The correct option is A $1596$
$a_{8} + b_{8} + c_{8} + \dots + h_{8} = (a_{1} + a_{2} + a_{3} + \dots + a_{7}) + (b_{1} + b_{2} + b_{3} + \dots + b_{7}) + (c_{1} + c_{2} + c_{3} + \dots + c_{7}) + (d_{1} + d_{2} + d_{3} + \dots + d_{7}) + (e_{1} + e_{2} + e_{3} + \dots + e_{7}) + (f_{1} + f_{2} + f_{3} + \dots + f_{7}) + (g_{1} + g_{2} + g_{3} + \dots + g_{7}) + (h_{1} + h_{2} + h_{3} + \dots + h_{7})$

$a_{8} + b_{8} + c_{8} + \dots + h_{8} = (a_{1} + b_{1} + c_{1} + \dots + h_{1}) + (a_{2} + b_{2} + c_{2} + \dots + h_{2}) + (a_{3} + b_{3} + c_{3} + \dots + h_{3}) + (a_{4} + b_{4} + c_{4} + \dots + h_{4}) + (a_{5} + b_{5} + c_{5} + \dots + h_{5}) + (a_{6} + b_{6} + c_{6} + \dots + h_{6}) + (a_{7} + b_{7} + c_{7} + \dots + h_{7})$

$a_{8} + b_{8} + c_{8} + \dots + h_{8} = 1 + 2 + 3 + 4 + \dots \dots + 56 = \frac{56 \times 57}{2} = 1596 [Sum of first 56 natural numbers]$

Option B is correct

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