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प्रश्न
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
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उत्तर
Given, t2 = 14 and t3 = 18
`=>` d = t3 – t2
= 18 – 14
= 4
Now t2 = 14
`=>` a + d = 14
`=>` a = 14 – 4
`=>` a = 10
Sum of n terms of an A.P. = `n/2[2a + (n - 1)d]`
∴ Sum of first 51 terms of an A.P. = `51/2 [2 xx 10 + 50 xx 4]`
= `51/2 [20 + 50 xx 4]`
= `51/2 [20 + 200]`
= `51/2 xx 220`
= 51 × 110
= 5610
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संबंधित प्रश्न
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
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Find the sum of natural numbers between 1 to 140, which are divisible by 4.
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`
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Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
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