find three consecutive numbers if three times the middle number is greater than the sum of the first and the last number by 176

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## Answer :-

## Given :-

## To Find :-

## Solution :-

Let the three consecutive numbers be x , x + 1 , x + 2.

According to the question :-

3 × middle term = first term + last term + 176

→ 3 ( x + 1 ) = x + x + 2 + 176

→ 3x + 3 = 2x + 178

→ 3x – 2x = 178 – 3

→ x = 175

→ x + 1 = 175 + 1 = 176

→ x + 2 = 175 + 2 = 177

## The three consecutive numbers are 175 , 176 , 177.

## Verification :-

→ LHS = 3 ( x + 1 )

→ LHS = 3 ( 175 + 1 )

→ LHS = 3 × 176

→ LHS = 528

→ RHS = x + x + 2 + 176

→ RHS = 175 + 175 + 2 + 176

→ RHS = 175 + 177 + 176

→ RHS = 528

LHS = RHS

Hence verified.