Advertisements
Advertisements
प्रश्न
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Advertisements
उत्तर
an = 9 − 5n
a1 = 9 − 5 × 1
= 9 − 5
= 4
a2 = 9 − 5 × 2
= 9 − 10
= −1
a3 = 9 − 5 × 3
= 9 − 15
= −6
a4 = 9 − 5 × 4
= 9 − 20
= −11
It can be observed that
a2 − a1 = −1 − 4 = −5
a3 − a2 = −6 − (−1) = −5
a4 − a3 = −11 − (−6) = −5
i.e., ak + 1 − ak is same every time. Therefore, this is an A.P. with common difference as −5 and first term as 4.
`S_n = n/2 [2a + (n - 1)d]`
`S_15 = 15/2 [2(4) + (15 - 1) (-5)]`
= `15/2 [8 + 14(-5)]`
= `15/2 (8 - 70)`
= `15/2 (-62)`
= 15 × (-31)
= -465
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum 25 + 28 + 31 + ….. + 100
Find the sum of all odd natural numbers less than 50.
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 next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Find the sum of all 2 - digit natural numbers divisible by 4.
The nth term of an A.P., the sum of whose n terms is Sn, is
The common difference of an A.P., the sum of whose n terms is Sn, is
Find the sum of the first 10 multiples of 6.
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
Find the sum of all even numbers from 1 to 250.
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 nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
