1.

Sum of first 55 terms in an A.P. is 3300, find its 28th term. 

Answer»

For an A.P., let a be the first term and d be the common difference. 

S55 =3300 …[Given] 

Since, Sn = n/2 [2a + (n – 1)d] 

∴ S55 = 55/2 [2a + (55 – 1)d]

∴ 3300 = 55/2 (2a + 54d)

∴ 3300 = 55/2 x 2(a + 27d)

∴ 3300 = 55(a + 27d)

∴  a + 27d = 3300/5

∴ a + 27d = 60   ....(i)

Now, tn = a + (n - 1)d

∴ t28 = a + ( 28 - 1)d = a + 27d

∴ t28 = 60   ... [Frtom (i)]

∴ 28th terms of the A.P is 60.



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