Advertisements
Advertisements
Question
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Advertisements
Solution
a = 8, an = 62, Sn = 210
an = a + (n – 1)d
62 = 8 + (n – 1)d
(n – 1)d = 62 – 8 = 54 ...(i)
Sn = `n/(2)[2a + (n - 1)d]`
210 = `n/(2)[2 xx 8 + 54]` ...[From (i)]
420 = n(16 + 54)
⇒ 420 = 70n
n = `(420)/(70)` = 6
∴ (6 – 1)d = 54
⇒ 5d = 54
⇒ d = `(54)/(5)`
Hence d = `(54)/(5) and n = 6`.
APPEARS IN
RELATED QUESTIONS
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 the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3, ..., 4 1/3.`
Which term of the AP 21, 18, 15, ... is zero?
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
Q.5
Q.6
If a = 6 and d = 10, then find S10.
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
