Advertisements
Advertisements
Question
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Solution
0.6, 1.7, 2.8, …, to 100 terms
For this A.P.,
a = 0.6
d = a2 − a1
= 1.7 − 0.6
d = 1.1
n = 100
We know that
Sn = `n/2[2a+(n-1)d]`
S100 = `100/2[2(0.6)+(100 - 1)1.1]`
= 50[1.2 + (99) × (1.1)]
= 50[1.2 + 108.9]
= 50[110.1]
= 5505
Thus, the required sum of first 100 terms is 5505.
RELATED QUESTIONS
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
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 the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
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.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
Which term of the sequence 114, 109, 104, ... is the first negative term?
The first term of an A.P. is p and its common difference is q. Find its 10th term.
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
Sum of 1 to n natural number is 45, then find the value of n.
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?
The sum of 41 terms of an A.P. with middle term 40 is ______.
