Advertisements
Advertisements
प्रश्न
Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
(iv) 2, 8, 18, 32,..........
उत्तर
The given progression `sqrt(2)`, `sqrt(8)`, `sqrt(18)`, `sqrt(32)`,..........
This sequence can be written as `sqrt(2)` ,2 `sqrt(2)` ,3 `sqrt(2)` ,4 `sqrt(2)`,........
Clearly, 2 `sqrt(2)` - `sqrt(2)` = 3 `sqrt(2)` - 2 `sqrt(2)` = 4 `sqrt(2)` - 3 `sqrt(2)` = `sqrt(2)` (Constant)
Thus, each term differs from its preceding term by 2, So, the given progression is an AP.
First term =`sqrt(2)`
Common difference = `sqrt(2)`
Next tern of the AP = 4 `sqrt(2)` + `sqrt(2)` = 5 `sqrt(2)` = 50
APPEARS IN
संबंधित प्रश्न
Find the number of terms in the following A.P.
`18,15 1/2, 13`, ..., – 47
Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?
Which term of the A.P. 8, 14, 20, 26, ... will be 72 more than its 41st term?
Find the indicated terms in the following sequences whose nth terms are:
an = 5n - 4; a12 and a15
Which term of the A.P. 84, 80, 76, ... is 248?
The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A.P.
The nth term of an AP is (3n +5 ). Find its common difference.
What is the common difference of an AP in which a18 – a14 = 32?
Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is ______.
Justify whether it is true to say that the following are the nth terms of an AP.
3n2 + 5
