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प्रश्न
Find t21, if S41 = 4510 in an A.P.
उत्तर
For an A.P., let a be the first term and d be the common difference.
S41 = 4510 ......[Given]
Since Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`,
S41 = `41/2 [2"a" + (41 - 1)"d"]`
∴ 4510 = `41/2 (2"a" + 40"d")`
∴ 4510 = `41/2 xx 2 ("a" + 20"d")`
∴ 4510 = 41(a + 20d)
∴ a + 20d = `4510/41`
∴ a + 20d = 110 .....(i)
Now, tn = a + (n – 1)d
∴ t21 = a + (21 – 1)d
= a + 20d
∴ t21 = 110 ......[From (i)]
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