CLASS 10TH NCERT SOLUTIONS CH 5 MATHS QUESTIONS 3 & 4 WITH ANSWER EX 5.1
प्रश्न - (3 ) निम्नलिखित में से प्रत्येक A . P के लिए प्रथम पद तथा सर्वान्तर लिखिए ?
( i ) 3 , 1 , -1 , -3 , . . . . . . . . (ii ) -5 , -1 , 3 , 7 , . . . .. .. ..
(iii ) 1 / 3 , 5 / 3 , 9 / 3 , 13 / 3 , . . .. .. .. (iv) 0. 6 , 1. 7 , 2. 8 , 3. 9 .. . .. .. ..
हल : ( i ) 3 , 1 , -1 , -3 , . . . . . . . .
प्रथम पद a = 3 तथा सर्वान्तर d = 1 - 3 = -2 (दूसरे पद में से पहले पद को घटाकर निकलते हे। )
(ii ) -5 , -1 , 3 , 7 , . . . .. .. ..
प्रथम पद a = -5 तथा सर्वान्तर d = -1 - (- 5 ) = -1 + 5 = 4
(iii ) 1 / 3 , 5 / 3 , 9 / 3 , 13 / 3 , . . .. .. ..
प्रथम पद = 5 / 3 , तथा सर्वान्तर d = 5 /3 - 1 / 3 = 5 -1 / 3 = 4 / 3
(iv) 0. 6 , 1. 7 , 2. 8 , 3. 9 .. . .. .. ..
प्रथम पद = 0. 6 , तथा सर्वान्तर d = 1. 7 - 0. 6 = 1.1
प्रश्न - (4) निम्नलिखित में से कौन - कौन A . P हे। यदि कोई A . P हे , तो इसका सर्वान्तर ज्ञात कीजिये और इनके तीन पद और लिखिए ?
हल :
=> a2 - a1 = 4 - 2 = 2
a3 - a2 = 8 - 4 = 4
a4 - a3 = 16 - 8 = 8
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
a2 - a1 = 5 / 2 - 2 = 1 / 2
a3 - a2 = 3 - 5 / 2 = 1 / 2
a4 - a3 = 7 / 2 - 3 = 1 / 2
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
a2 - a1 = a3 - a2 = a4 - a3 = 1 / 2 = d
अगले तीन पद निम्न प्रकार हे।
=> a5 = 7 / 2 + 1 / 2 = ( 7 + 1 ) / 2 = 8 / 2 = 4 = पांचवा पद
=> a6 = 4 + 1 / 2 = 9 / 2 = छटा पद
=> a7 = 9 / 2 + 1 / 2 = 10 / 2 = 5 =सातवां पद
a2 - a1 = -3. 2 - ( -1.2) = -3 . 2 + 1. 2 = -2
a3 - a2 = - 5. 2 - (-3 . 2) = - 2
a4 - a3 = -7. 2 - ( - 5 . 2 ) = -2
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
a2 - a1 = a3 - a2 = a4 - a3 = - 2 = d =सर्वान्तर
अगले तीन पद निम्न प्रकार हे।
a5 = -7. 2 + (-2 ) = -7. 2 - 2 . 0 = -9. 2
a6 = -9.2 - 2 = -11 . 2
a7 = - 11. 2 - 2 . 0 = -13. 2
अगले तीन पद निम्न प्रकार हे।
पांचवा पद => a5 = a + 4d = -10 + 4 * 4 = -10 + 16 = 6
छटवां पद => a6 = a + 5d = -10 + 5 * 4 = -10 + 20 = 10
सातवां पद => a7 = a + 6d = -10 + 6 * 4 = -10 + 24 = 14 : उत्तर
अगले तीन पद , a5 = a + 4d = 3 + 4\/2
a6 = a + 5d = 3 + 5\/2
a7 = a + 6d = 3 + 6\/2 : उत्तर
यह A . P नहीं हे।
अगले तीन पद निम्न प्रकार हे।
- 12 - 4 = - 16 , - 16 - 4 = - 20 , - 20 - 4 = - 24
अतः यह एक A . P हे। जिसका सर्वान्तर d = -4 हे। तथा अगले तीन पद -16 , - 20 , -24 हे।
अगले तीन पद हे ,
- 1 / 2 + 0 = - 1 / 2 , - 1 / 2 + 0 = - 1 / 2 , - 1 / 2 + 0 = - 1 / 2
अतः सर्वान्तर d = 0 तथा अगले तीन पद - 1 / 2 , - 1 / 2 , - 1 / 2 हे।
ENGLISH TRANSLATION :
CLASS 10TH NCERT SOLUTIONS CH 5 MATHS QUESTIONS 3 & 4 WITH ANSWER EX 5.1
Question - (3) Each of the following A. Write the first term and differential for P?
( i ) 3 , 1 , -1 , -3 , . , , , , , , , (ii) -5 , -1 , 3 , 7 , . , , ,
(iii) 1 / 3 , 5 / 3 , 9 / 3 , 13 / 3 , . , .. .. .. (iv) 0. 6 , 1. 7 , 2. 8 , 3. 9 .. . ,
Solution : ( i ) 3 , 1 , -1 , -3 , . , , , , , , ,
The first term a = 3 and the differential d = 1 - 3 = -2 (The second term is obtained by subtracting the first term. )
(ii) -5 , -1 , 3 , 7 , . , , ,
First term a = -5 and second term d = -1 - (-5 ) = -1 + 5 = 4
(iii) 1 / 3 , 5 / 3 , 9 / 3 , 13 / 3 , . , ,
First term = 5 / 3 , and second term d = 5 /3 - 1 / 3 = 5 -1 / 3 = 4 / 3
(iv) 0. 6 , 1. 7 , 2. 8 , 3.9 .. . ,
First term = 0. 6 , and second term d = 1. 7 - 0. 6 = 1.1
Question - (4) Which of the following - A. P is If any A. P is , then find its paradox and write its three more terms?
solve : 
a2 - a1 = 4 - 2 = 2
a3 - a2 = 8 - 4 = 4
a4 - a3 = 16 - 8 = 8
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
Hence it is not an AP.
solve : a2 - a1 = 5 / 2 - 2 = 1 / 2
a3 - a2 = 3 - 5 / 2 = 1 / 2
a4 - a3 = 7 / 2 - 3 = 1 / 2
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
a2 - a1 = a3 - a2 = a4 - a3 = 1 / 2 = d
The next three terms are as follows.
=> a5 = 7 / 2 + 1 / 2 = ( 7 + 1 ) / 2 = 8 / 2 = 4 = Fifth Term
=> a6 = 4 + 1 / 2 = 9 / 2 = Sixth term
=> a7 = 9 / 2 + 1 / 2 = 10 / 2 = 5 = Seventh term
SOLVE : a2 - a1 = -3. 2 - ( -1.2) = -3 . 2 + 1. 2 = -2
a3 - a2 = - 5. 2 - (-3 . 2) = - 2
a4 - a3 = -7. 2 - ( - 5 . 2 ) = -2
.. . .. . .. . .. . . .. .. .. . .. . . .. ..
a2 - a1 = a3 - a2 = a4 - a3 = - 2 = d
The next three terms are as follows.
a5 = -7. 2 + (-2 ) = -7. 2 - 2 . 0 = -9. 2
a6 = -9.2 - 2 = -11 . 2
a7 = - 11. 2 - 2 . 0 = -13. 2 :answer
The next three terms are as follows.
Fifth term => a5 = a + 4d = -10 + 4 * 4 = -10 + 16 = 6
6th term => a6 = a + 5d = -10 + 5 * 4 = -10 + 20 = 10
Seventh term => a7 = a + 6d = -10 + 6 * 4 = -10 + 24 = 14 : Answer
Next three terms, a5 = a + 4d = 3 + 4\/2
a6 = a + 5d = 3 + 5\/2
a7 = a + 6d = 3 + 6\/2 : Answer
Hence it is not an AP.
The next three terms are as follows.
- 12 - 4 = - 16 , - 16 - 4 = - 20 , - 20 - 4 = - 24
So this is an A. P is whose parallelogram is d = -4. And the next three terms are -16 , - 20 , -24.
The next three terms are
- 1/2 + 0 = - 1/2 , - 1/2 + 0 = - 1/2 , - 1/2 + 0 = - 1/2
Therefore, the terminal d = 0 and the next three terms are - 1/2 , - 1 / 2 , - 1 / 2 .
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