12 term of an ap is 43 and 17th term of an ap is 78find its 32nd term
Answers
a 12 = 43 ⇒ a + 11 d = 43
a 17 =78⇒ a+16d = 78
to eliminate d , a + 11d = 43
a + 16d =78
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we get, -5d = - 35
ie., d= 7
a + 11d = 43
a+11×7 =43
then, a32 = a +31 d
= -34 + 31×7
a32 = 183
Answer:
12th term of AP = 43
⇒ a + (n-1)d = 43
a + (12-1)d = 43
a + 11d = 43
a = 43 - 11d — (i)
17th term of AP = 78
⇒ a + (n-1)d = 78
a + (17-1)d = 78
a + 16d = 78
a = 78 - 16d — (ii)
Now we compare both the equations:-
Since we know that both the values stand for ‘a’, we can say that they are equal to each other.
43 - 11d = 78 - 16d
-11d + 16d = 78 - 43
5d = 35
d = 7
Now we find the value of ‘a’ by substituting the value of ‘d’ in equation (i):-
a = 43 - 11d
a = 43 - 11(7)
a = 43 - 77
a = -34
Now to find the 32nd term:-
Formula:-
a + (n-1)d
⇒ -34 + (32-1)7
-34 + (31)7
-34 + 217
183 Ans
The 32nd term of AP = 183
Hope it helps
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