Advertisements
Advertisements
Question
If x + 1, 3x and 4x + 2 are in A.P., find the value of x.
Solution
Here, we are given three terms which are in A.P.
First-term `(a_1) = x + 1`
Second term `(a_2) = 3x`
Third term `(a_3) = 4x + 2`
We need to find the value of x. So in an A.P. the difference of two adjacent terms is always constant. So we get
`d = a_2 - a_1`
d = (3x) - (x + 1)
d = 3x - x - 1
d = 2x - 1 .........(1)
Also
`d = a_3 - a_2`
d= (4x + 2) - (3x)
d = 4x - 3x + 2
d = x + 2 ......(2)
Now on equating (1) and (2) we get
2x - 1 = x + 2
2x - x = 2 + 1
x = 3
Therefore for x= 3 these three terms will form an A.P
APPEARS IN
RELATED QUESTIONS
Write the first three terms of the A.P. whose common difference is ‒3 and first term is 4.
If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n)
Write first four terms of the A.P. when the first term a and the common difference d are given as follows:
a = -1.25, d = -0.25
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
1, 3, 9, 27 …
For the following arithmetic progressions write the first term a and the common difference d:
`1/5, 3/5, 5/5, 7/5`
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
In the winter season let us take the temperature of Ooty from Monday to Friday to be in A.P. The sum of temperatures from Monday to Wednesday is 0°C and the sum of the temperatures from Wednesday to Friday is 18°C. Find the temperature on each of the five days.
Find a and d for an A.P., 1, 4, 7, 10,.........
Determine k so that k2 + 4k + 8, 2k2 + 3k + 6, 3k2 + 4k + 4 are three consecutive terms of an AP.
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers
The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.
