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प्रश्न
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
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उत्तर
2, 7, 12, …, to 10 terms
For this A.P.,
a = 2
d = a2 − a1
d = 7 − 2
d = 5
n = 10
We know that,
Sn = `n/2 [2a + (n - 1) d]`
S10 = `10/2 [2(2) + (10 - 1) × 5]`
= 5[4 + (9) × (5)]
= 5 × 49
= 245
Thus, the sum of first 10 terms is 245.
संबंधित प्रश्न
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An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
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Q.3
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
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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`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
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