T₇=12,T₁₂=72,Find AP. If Tn, Tm are as given below.
Answers
Dear Student,
Answer: AP is -60,-48, -36,-24, -12, 0, 12 ...
Solution:
we know that nth element of AP is given as = a+ (n-1) d
T₇=12
i.e. 12=a+ ( 7-1) d
12 = a+6d
a+6d = 12 .....eq1
T₁₂=72
i.e 72 = a+ (12-1)d
a+11d = 72 .......eq2
Subtract eq2 from eq1
a+6d-a-11d = 12-72
-5d = - 60
5d = 60
d = 12
put value of d in any of the equation
a+6d = 12
a+ 72 = 12
a = 12-72
a = -60
First element is -60 , common difference is 12
AP is a, a+d ,a+2d, a+3d ...
-60, -60+12, -60+12(2) , -60+12(3), -60+12(4),....
-60,-48, -36,-24, -12, 0, 12 ...
Hope it helps you.
Given that 7th term of an AP T7 = 12.
We know that nth term of an AP An = a + (n - 1) * d.
Now,
T7 = a + (n - 1) * d
12 = a + (7 - 1) * d
12 = a + 6d ---- (1)
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Given that 12th term of an AP T12 = 72
= > 72 = a + (12 - 1) * d
= > 72 = a + 11d ----- (2)
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On solving (1) & (2), we get
= > a + 6d = 12
= > a + 11d = 72
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-5d = -60
d = 12.
Substitute d = 12 in (1), we get
= > a + 6d = 12
= > a + 6(12) = 12
= > a + 72 = 12
= > a = 12 - 72
= > a = -60
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Therefore, The AP is -60, -60 + 12......
= > -60, -48, -36....
Hope this helps