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
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 3 + 4n
Also, find the sum of the first 15 terms.
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
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.
