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]

∴ S₅₅ = `55/2`[2a + (55 – 1) d]

∴ 3300 = `55/2`[2a + 54d]

∴ 3300 = `55/2` × 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.