Question

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

Answer 1

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

S₅₅ = 3300   ...[Given]

We know that, 

Since `S_n = n/2 [2a + (n - 1)d]`

∴ `S_55 = 55/2 [2a + (55 - 1)d]`

∴ `3300 = 55/2 [2a + 54d]`

∴ `3300 = 55/2 xx 2[a + 27d]`

∴ 3300 = 55[a + 27d]

∴ a + 27d = `3300/55`

∴ a + 27d = 60   ...(i)

Now, t_n = a + (n – 1)d

∴  t₂₈ = a + (28 – 1)d

∴ t₂₈ = a + 27d

∴ t₂₈ = 60   ...[From (i)]

∴ 28^th term of A.P. is 60.