Advertisements
Advertisements
प्रश्न
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
Advertisements
उत्तर
`1/15, 1/12, 1/10,` ......, to 11 terms
For this A.P.,
a = `1/15`
n = 11
d = a2 - a1
= `1/12-1/15`
= `(5-4)/60`
= `1/60`
We know that
Sn = `n/2[2a + (n -1)d]`
S11 = `11/2[2(1/15)+(11-1)1/60]`
S11 = `11/2[2/5+10/60]`
S11 = `11.2[2/15+1/6]`
S11 = `11/2[(4+5)/30]`
S11 = `(11/2)(9/30)`
S11 = `33/20`
Thus, the required sum of first 11 terms is `33/20`.
APPEARS IN
संबंधित प्रश्न
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
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 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
If (2p +1), 13, (5p -3) are in AP, find the value of p.
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Write the nth term of an A.P. the sum of whose n terms is Sn.
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
Q.6
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment
First four terms of the sequence an = 2n + 3 are ______.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
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))`
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
