Advertisements
Advertisements
प्रश्न
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the sum 3 + 11 + 19 + ... + 803
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
Which term of the sequence 114, 109, 104, ... is the first negative term?
Q.5
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
How many terms of the AP: –15, –13, –11,... are needed to make the sum –55? Explain the reason for double answer.
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
