Q. 144.7( 6 Votes )

In an A.P. a = 8, Tn= 33, Sn = 123, find d and n.

Answer :

We have a = 8


We know that, Tn = a + (n – 1)d


And from the question we can say that, Tn= 53


So we get,


33 = a + (n – 1)d


Putting value of a in the above equation,


33 = 8 + (n – 1)d


(n – 1)d = 33 – 8


(n – 1)d = 25


Now we have that, Sn = × (2a + (n – 1)d)


From the question we can say that, Sn = 123


So, we have,


123 = × (2a + (n – 1)d)


246 = n × (2a + (n – 1)d)


now we have a = 8 and (n – 1)d = 25, so we put them in the above equation,


246 = n × (2(8) + 25)


246 = n × (16 + 25)


246 = n × (31)


n= = 6


n = 6


now, we know that, (n – 1)d = 25


we put the value of n in the above equation, we get


(6 – 1)d = 25


5d = 25


d = 5


for the given A.P, value of n is 6 and value of d is 5.


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