Advertisements
Advertisements
Question
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
Advertisements
Solution
It is given that (3y - 1),(3y +5) and (5y +1) are three consecutive terms of an AP.
∴ (3y +5 ) -(3y-1) = (5y+1) -(3y+5)
⇒ 3y +5-3y +1 = 5y +1 -3y -5
⇒ 6 = 2y - 4
⇒ 2y = 6+4 =10
⇒ y = 5
Hence, the value of y is 5.
APPEARS IN
RELATED QUESTIONS
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
Which term of AP 72,68,64,60,… is 0?
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
If the common differences of an A.P. is 3, then a20 − a15 is
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 the sum of first p term of an A.P. is ap2 + bp, find its common difference.
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
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 n terms of an A.P. is 3n2. The second term of this A.P. is ______.
