Advertisements
Advertisements
Question
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers
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 sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
In an AP given a3 = 15, S10 = 125, find d and a10.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative 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.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
The sum of all two digit odd numbers is ______.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
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?
