16.14.12... या अंकगणिती श्रेढीत किती पदे घेतल्यास बेरीज 60 येईल? आपणाला दोन उत्तरे का
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Answers
Given : 16. 14. 12 . . . अंकगणिती श्रेढीत
AP series
To Find : How many numbers adds upto 60
किती पदे घेतल्यास बेरीज 60 येईल
Solution:
16. 14. 12 . . .
a = 16
d = - 2
Sₙ = (n/2)(2a + (n - 1)d)
= (n/2)(2(16) + (n - 1)(-2))
= n ( 16 - n + 1)
= n ( 17 - n)
= -n² + 17n
-n² + 17n = 60
=> n² - 17n + 60 = 0
=> n² - 12n - 5n + 60 = 0
=> (n - 12)( n - 5) = 0
=> n = 12 , n = 5
5 numbers or 12 numbers adds upto 60
Next 7 numbers out of 12 numbers adds upto 0 as few are +ve numbers and few are negative numbers
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