Advertisements
Advertisements
प्रश्न
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...
उत्तर
a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...
Here,
First term (a) = a + b
`a_1 = ( a + 1) + b`
`a_1 = ( a + 1) + (b +1)`
Now, for the given to sequence to be an A.P,
Common difference (d) ` = a_1 - a = a_2 -a_1`
Here,
`a_1 -a = a + 1 + b - a- b`
= 1
Also,
`a_2 - a_1 = a+1+b+1-a-1-b`
= 1
Since `a_1 - a = a_2 -a_1`
Hence, the given sequence is an A.P and its common difference is d = 1
APPEARS IN
संबंधित प्रश्न
If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13th term is zero
In the following situation, involved make an arithmetic progression? and why?
The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km.
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
2, 4, 8, 16 …
If the 10th term of an A.P. is 52 and the 17th term is 20 more than the 13th term, find the A.P.
Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.
The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15thterm.
First term a and common difference d are given below. Find the corresponding A.P.
a = `3/4`, d = `1/2`
Find first four terms of an A.P., whose first term is 3 and common difference is 4.
Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
