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

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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