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Question
Sum of first 55 terms in an A.P. is 3300, find its 28th term.
Solution
For an A.P., let a be the first term and d be the common difference.
S55 = 3300 ......[Given]
We know that,
Since 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]
∴ a + 27d = `3300/55`
∴ a + 27d = 60 ......(i)
Now, tn = a + (n – 1)d
∴ t28 = a + (28 – 1)d
∴ t28 = a + 27d
∴ t28 = 60 .......[From (i)]
∴ 28th term of A.P. is 60.
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