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प्रश्न
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
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उत्तर
2020 is a leap year.
In February month there are 29 days.
n = 29
On the first day of the month Kavita invested ₹20.
On the second day, she invested ₹40.
On the third day, she invested ₹60.
Kavita's investment is in A.P. 20, 40, 60, ....
a = 20, n = 29, d = 20
Now, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_29 = 29/2 [2(20) + (29 - 1)(20)]`
= `29/2 [40 + 28 xx 20]`
= `29/2 [40 + 560]`
= `29/2 [600]`
= 29 × 300
= 8700
∴ Total savings of Kavita in the month of February 2020 is ₹ 8,700.
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Q.14
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"]`
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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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