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प्रश्न
For an given A.P., t7 = 4, d = −4, then a = ______.
विकल्प
6
7
20
28
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उत्तर
For an given A.P., t7 = 4, d = −4, then a = 28.
Explanation:
Given,
t7 = 4
d = −4
Now,
tn = a + (n − 1)d
t7 = a + (7 − 1)d
⇒ 4 = a + 6(−4)
⇒ 4 = a − 24
⇒ a = 4 + 24
⇒ a = 28
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First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
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Q.15
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`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
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