Advertisements
Advertisements
प्रश्न
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
Advertisements
उत्तर
The given sequence is `1/6, 1/4, 1/3`
The above sequence is an A.P.
∴ a = `1/6`
d = `1/4 -1/6 = ((6 - 4)/(6 xx 4))= 2/24 = 1/12`
The next four terms of the sequence are
t4 = t3 + d = `1/3 + 1/12 = 5/12`
t5 = t4 + d = `5/12 + 1/12 = 6/12 = 1/2`
t6 = t5 + d = `1/2 + 1/12 = 7/12`
t7 = t6 + d = `7/12 + 1/12 = 8/12 = 2/3`
Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`
= `"n"/2 [2(1/6) + ("n" - 1)(1/12)]`
= `"n"/2 (1/3 + 1/12 "n" - 1/12)`
= `"n"/2("n"/12 + 1/4)`
∴ Sn = `("n"("n" + 3))/24`
APPEARS IN
संबंधित प्रश्न
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
How many multiples of 4 lie between 10 and 250?
Find the sum of first 40 positive integers divisible by 6.
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
Find the sum of first 12 natural numbers each of which is a multiple of 7.
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
If (2p – 1), 7, 3p are in AP, find the value of p.
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
If 18, a, b, −3 are in A.P., the a + b =
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
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.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
