What number is to be added to the product of any two consecutive terms of an arithmetic sequence of common difference 6 so as to get a perfect square? Justify your answer.
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Given : number is to be added to the product of any two consecutive terms of an arithmetic sequence of common difference 6 so as to get a perfect square
To Find : the number to be added
Solution:
Two numbers are a , a + 6
Hence Product = a² + 6a
= a² + 6a + 9 - 9
= (a + 3)² - 9
a² + 6a = (a + 3)² - 9
Hence 9 must be added to a² + 6a to get perfect square
other way
Let say two terms are
a- 3 , a + 3
Then Product = a² - 9
Hence n should be added to get a²
Learn More:
How to derive sum of n terms of an A.P? - Brainly.in
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In an A.P if sum of its first n terms is 3n square +5n and it's Kth term ...
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Step-by-step explanation:
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