The sum of the first 55 terms of an A. P. is 3300. Find the 28th term.


7. The sum of the first 55 terms of an A. P. is 3300. Find the 28th term.

Sol. S55 = 3300 [Given]

Sn = n/2[2a + (n – 1)d]

S55 = 55/2[2a + (55 – 1) d]

3300 = 55/2[2a + 54d]

3300 = 55/2 × 2[a + 27d]

3300 = 55 [a + 27d]

3300/55 = a + 27d

a + 27d= 60 ......(i)


Now, tn = a + (n – 1) d


 t28 = a + (28 – 1) d

t28 = a + 27d

t28 = 60 [From (i)]

Twenty eighth term of A.P. is 60.