a2=13,a4=3 find a1,a3
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Question: In an AP, a2 = 13, a4 = 3 find a1 and a3
Sol: Given 2nd term = 13
2nd term = a + d
∴a + d = 13 ------------------(1)
Given 4th term = 3
And 4th term = a + 3d
∴a + 3d = 3 -------------------(2)
Solving (1) and (2)
subtracting (2) from (1)
a + d = 13
a + 3d=3
⇒ -2d = 10
⇒ d = 10/-2
∴d = -5
Substituting d in eq 1
⇒a + d = 13
⇒a + (-5) = 13
⇒a-5b=13
⇒a = 13+5
⇒a = 18
a = a1 = 18
a3 = a+2d
= 18 + 2(-5)
=18-10
a3=8
Sol: Given 2nd term = 13
2nd term = a + d
∴a + d = 13 ------------------(1)
Given 4th term = 3
And 4th term = a + 3d
∴a + 3d = 3 -------------------(2)
Solving (1) and (2)
subtracting (2) from (1)
a + d = 13
a + 3d=3
⇒ -2d = 10
⇒ d = 10/-2
∴d = -5
Substituting d in eq 1
⇒a + d = 13
⇒a + (-5) = 13
⇒a-5b=13
⇒a = 13+5
⇒a = 18
a = a1 = 18
a3 = a+2d
= 18 + 2(-5)
=18-10
a3=8
yasummu:
In general series 2nd term = a+d but 2nd term is given as 13
So a+d = 13, similarly 4th term = a+3d but given as 3. so a+3d = 3, now we are solving these two equations. Here we are subtracting equation 1 from the 2. We get -2d = 10, this is answer we get by subtracting 1 and 2. we get d that is the common difference. then we substitute value of d in equation 1 by this we get value of a
With a and d we can write the 1st and 3rd terms .
but a+d kyu liye
1st term = a and 3rd term = a+2d
General series of AP is a, a+d, a+2d, a+3d,....... is main 2nd term a+d hai isliye
okkkk i understood
thankx
your welcome magar itni mushkil huyee sorry
and please mark as the best if you feel to
Answered by
2
Answer:
Given AP
a
2
=13 a
4
=3
a
2
=a+(n−1)d=a+d
a
4
=a+(4−1)d=a+3d
Here a+d=13 __ (1)
a+3d=3 __ (2)
(2) - (1) ⇒2d=−10
d=−5
substitute d= -5 in (1)
a-5 = 13
a = 18
∴a
1
=a=18
a
3
=a+2d=18+2(−5)
=8
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