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The sum of five consecutive odd numbers is equal to 175. What is the sum of the second largest number and the square of the smallest number among them together?

Correct Answer:

Explanation:

Method 1 to solve this question.
Let p be the first odd number.
Then next odd number is p + 2.
According to question,
Sum of five consecutive odd numbers 175
⇒ p + p + 2 + p + 4 + p + 6 + p + 8 = 175
⇒ 5p + 20 = 175
⇒ p = (175 - 20)/5 = 31
According to question,
Sum of the second largest and square of smallest one = (31 + 6) + (31)2
Sum of the second largest and square of smallest one = 37 + 961 = 998
Method 2 to solve this question.
Let p be the even number.
Then next odd number is p + 1. so on p + 3 , p + 5................ P + 9
According to question,
Sum of five consecutive odd numbers 175
⇒ p + 1 + p + 3 + p + 5 + p + 7 + p + 9 = 175
⇒ 5p + 25 = 175
⇒ p = (175 - 25)/5
⇒ p = (150)/5
⇒ p = 30
First odd number = p + 1 = 30 + 1 = 31
According to question,
Sum of the second largest and square of smallest one = (30 + 7) + (30 + 1)2
Sum of the second largest and square of smallest one = 37 + 961 = 998


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