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प्रश्न
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
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उत्तर
Let common difference be d.
a = 3
Sum of first n terms of an A.P. = `n/2(a + 1)`
Given,
The sum of the first 8 terms is twice the sum of the first 5 terms.
∴ `8/2(a + a_8) = 2 xx 5/2(a + a_5)`
⇒ 4[a + a + (8 − 1)d] = 5[a + a + (5 − 1)d]
⇒ 4[2a + 7d] = 5[2a + 4d]
⇒ 4[2 × 3 + 7d] = 5[2 × 3 + 4d]
⇒ 4[6 + 7d] = 5[6 + 4d]
⇒ 24 + 28d = 30 + 20d
⇒ 28d − 20d = 30 − 24
⇒ 8d = 6
⇒ d = `6/8`
⇒ d = `3/4`
संबंधित प्रश्न
In an AP given a3 = 15, S10 = 125, find d and a10.
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)]
Find the sum of all 3-digit natural numbers, which are multiples of 11.
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
If (2p +1), 13, (5p -3) are in AP, find the value of p.
In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference
If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Q.6
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
