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प्रश्न
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
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उत्तर
Given that,
`\implies` an = 5 + 6n
We have,
`\implies` a1 = 5 + 6(1) = 11
`\implies` a2 = 5 + 6(2) = 17
So, a = 11, d = 6
Sum of first 25 terms = `n/2(2a + (n - 1)d)`
= `25/2[2(11) + (25 - 1)6]`
= `25/2[22 + 144]`
= `25/2[166]`
= 2075
Now, a20 = a + 19d
= 11 + 19(6)
= 125
`\implies` a45 = a + 19d
= 11 + 44(6)
= 275
Required ratio = `a_20/a_45`
= `125/275`
= `5/11`
Ratio is 5:11.
संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
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