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प्रश्न
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
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उत्तर
The given sequence is `1/6, 1/4, 1/3`
The above sequence is an A.P.
∴ a = `1/6`
d = `1/4 -1/6`
= `(3 - 2)/12`
= `1/12`
The next four terms of the sequence are
t4 = t3 + d
= `1/3 + 1/12`
= `5/12`
t5 = t4 + d
= `5/12 + 1/12`
= `6/12`
= `1/2`
t6 = t5 + d
= `1/2 + 1/12`
= `7/12`
t7 = t6 + d
= `7/12 + 1/12`
= `8/12`
= `2/3`
`S_n = n/2 [2a + (n - 1)d]`
= `n/2 [2(1/6) + (n - 1)(1/12)]`
= `n/2 (1/3 + 1/12 n - 1/12)`
= `n/2(n/12 + 1/4)`
∴ `S_n = (n(n + 3))/24`
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Q.16
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Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
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