NCERT MATHS CLASS 10TH EXERCISE 5.2 QUESTION 1 SOLUTION CHAPTER 5 ARITHMETIC PROGRESSION
प्रश्न - (1 ) निम्नलिखित सारणी में रिक्त स्थानों को भरिये , जहाँ A . P का प्रथम पद a , सर्वान्तर d और n वां पद an हे :
(I ) a = 7 , d = 3 , n = 8 और an = ?
हल : यहाँ हम निम्न सूत्र का प्रयोग करेंगे।
an = a + ( n - 1 ) d
इस सूत्र में an अंतिम पद हे , a प्रथम पद , n = कुल पदों की संख्या तथा d सर्वान्तर हे।
an = 7 + ( 8 - 1 ) * 3
=> an = 7 + 7 * 3
=> an = 7 + 21
=> an = 28 : उत्तर
(ii ) यहाँ a = -18 , d = ?, n = 10 और an = 0
हल : an = a + ( n - 1 ) d
=> 0 = -18 + ( 10 - 1 ) * d
=> 0 = -18 + 9 d
=> 18 = 9d
=> 18 / 9 = d
=> 2 = d
या
=> d = 2
(iii ) यहाँ a = ? , d = -3 , n = 18 और an = -5
हल : an = a + ( n - 1 ) d
=> -5 = a + ( 18 - 1 ) * (-5 )
=> -5 = a + 17 * (-5 )
=> -5 = a - 85
=> -5 + 85 = a
=> 80 = a
=> a = 80
(iv) यहाँ a = -18.9 , d = 2.5 , n = ? और an = 3.6
हल : an = a + ( n - 1 ) d
3. 6 = -18.9 + (n - 1 ) * 2.5
=> 3. 6 + 18. 9 = (n - 1 ) * 2. 5
=> 22 .5 = (n - 1 ) * 2.5
=> 22.5 / 2.5 = n - 1
=> 9 = n - 1
=> 9 + 1 = n
=> 10 = n
=> n = 10 : उत्तर
(v ) यहाँ a = 3.5 , d = 0 , n = 105 और an = ?
हल : an = a + ( n - 1 ) d
=> an = 3.5 + (105 - 1 ) * 0
=> an = 3.5 + 104 * 0
=> an = 3.5 + 0
=> an = 3.5 : उत्तर
ENGLISH TRANSLATION :
Question - (1) Fill in the blanks in the following table, where A. The first term of P is a , the alternate d and the nth term an is :
(I) a = 7 , d = 3 , n = 8 and an = ?
Solution : Here we will use the following formula.
an = a + ( n - 1 ) d
In this formula, an is the last term, a is the first term, n = total number of terms and d is parallel.
an = 7 + ( 8 - 1 ) * 3
=> an = 7 + 7 * 3
=> an = 7 + 21
=> an = 28 : Answer
(ii) Here a = -18, d = ?, n = 10 and an = 0
Solution : an = a + ( n - 1 ) d
=> 0 = -18 + ( 10 - 1 ) * d
=> 0 = -18 + 9 d
=> 18 = 9d
=> 18 / 9 = d
=> 2 = d
either
=> d = 2
(iii) Here a = ? , d = -3 , n = 18 and an = -5
Solution : an = a + ( n - 1 ) d
=> -5 = a + ( 18 - 1 ) * (-5 )
=> -5 = a + 17 * (-5 )
=> -5 = a - 85
=> -5 + 85 = a
=> 80 = a
=> a = 80
(iv) Here a = -18.9 , d = 2.5 , n = ? and an = 3.6
Solution : an = a + ( n - 1 ) d
3. 6 = -18.9 + (n - 1 ) * 2.5
=> 3. 6 + 18.9 = (n - 1 ) * 2.5
=> 22.5 = (n - 1 ) * 2.5
=> 22.5 / 2.5 = n - 1
=> 9 = n - 1
=> 9 + 1 = n
=> 10 = n
=> n = 10 : Answer
(v) Here a = 3.5 , d = 0 , n = 105 and an = ?
Solution : an = a + ( n - 1 ) d
=> an = 3.5 + (105 - 1 ) * 0
=> an = 3.5 + 104 * 0
=> an = 3.5 + 0
=> an = 3.5 : Answer
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