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प्रश्न
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
विकल्प
–320
320
–352
–400
उत्तर
The sum of first 16 terms of the AP: 10, 6, 2,... is –320.
Explanation:
Given, AP is 10, 6, 2,...
Here,
First term a = 10,
Common difference,
d = – 4
∴ S16 = `16/2[2a + (16 - 1)d]` ...`[∵ S_n = n/2[2a + (n - 1)d]]`
= 8[2 × 10 + 15(– 4)]
= 8(20 – 60)
= 8(– 40)
= – 320
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संबंधित प्रश्न
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
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In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
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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