Advertisements
Advertisements
Question
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Advertisements
Solution
Here, we are given three terms,
First term (a1) = 2x
Second term (a2) = x + 10
Third term (a3) = 3x + 2
We need to find the value of x for which these terms are in A.P. So, in an A.P. the difference of two adjacent terms is always constant. So, we get,
d = a2 - a1
d = (x + 10 )- (2x)
d = x + 10 - 2x
d = 10 - x ...............(1)
Also,
d = a3 - a2
d = (3x + 2) - (x + 10 )
d = 3x + 2 - x -10
d = 2x - 8 ................(2)
Now, on equating (1) and (2), we get,
10 -x = 2x - 8
2x + x = 10 + 8
3x = 18
x = `18/3`
x = 6
Therefore, for x = 6 , these three terms will form an A.P.
APPEARS IN
RELATED QUESTIONS
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Find the sum of first n even natural numbers.
The Sum of first five multiples of 3 is ______.
Find the sum: 1 + 3 + 5 + 7 + ... + 199 .
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Find the sum of the first 10 multiples of 6.
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
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 ______.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
Three numbers in A.P. have the sum of 30. What is its middle term?
