the total of 3 continuous even numbers squares is 1208 .Find out the total of first two numbers squares?
Answers
Answer:
By definition, a number is even if it is divisible by 2. Therefore, we can denote an even number by 2n. The 5 consecutive even numbers can then be denoted by 2n, 2n+2, 2n+4, 2n+6, 2n+8. It is given that their sum is 260. Therefore we write,
2n + 2n+2 + 2n+4 + 2n+6 + 2n+8 = 260
Collecting all the 2n terms and the constant terms separately on LHS,
(2n + 2n + 2n + 2n + 2n) + (2+4+6+8) = 260
Adding the quantities within the two parentheses,
10n + 20 = 260
Dividing through out by 10,
n + 2 = 26 This yields the value
n = 24
Therefore, the 5 consecutive even numbers are
2n = 2x24 = 48
2n + 2 = 48 + 2 = 50
2n + 4 = 48 + 4 = 52
2n + 6 = 48 + 6 = 54
2n + 8 = 48 + 8 = 56
The above figures show that
The largest = 56
The smallest = 48
Therefore,
The largest + half of the square of the smallest
=56 + 1/2. 48² = 56 + 48x48/2 =56 + 48x24 = 56 + 1152
= 1208 (Proved)
Answer:
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