Q8 of 67 Page 74

The first term of an arithmetic progression is 8, nth term is 33 and sum of first n term is 123. Then find the n and common difference d.

Here first term a = 8, nth term = 33 and sn = 123
General nth term an is given as:
an = a + (n - 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



33 = 8 + (n -1) × d
25 = (n - 1) × d … (i)


Since the sum of n terms is
Sn =


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



So sum of first 25 terms S25
]
246 = n [ 16 + (n - 1) × d]
246 – 16 n = (n) × (n - 1) × d … (ii)


On dividing eq. (ii) from (i), we get,
⇒
⇒ (246 – 16n) = 25n
⇒ 25n + 16n = 246
⇒ 41n = 246
⇒ n = 6


Substituting the value of n in eq. (i), we get,
d = 5


Hence, Value of n is 6 and common difference is 5.


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