Advertisements
Advertisements
प्रश्न
Decide whether the given sequence 24, 17, 10, 3,...... is an A.P.? If yes find its common term (tn).
Advertisements
उत्तर
The given sequence is 24, 17, 10, 3,......
Here, t1 = 24, t2 = 17, t3 = 10, t4 = 3
∴ t2 – t1 = 17 – 24 = – 7
t3 – t2 = 10 – 17 = – 7
t4 – t3 = 3 – 10 = – 7
∴ t2 – t1 = t3 – t2 = ... = – 7 = d = constant
The difference between two consecutive terms is constant.
∴ The given sequence is an A.P.
tn = a + (n – 1)d
= 24 + (n – 1)(– 7)
= 24 – 7n + 7
= 31 – 7n
APPEARS IN
संबंधित प्रश्न
Find the sum of the following arithmetic series:
`7 + 10 1/2 + 14 + ... + 84`
Find the sum of the following arithmetic series:
34 + 32 + 30 + ... + 10
Find the sum of the following arithmetic series:
(–5) + (–8) + (–11) + ... + (–230)
Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.
Find the 27th term of the following A.P.
9, 4, –1, –6, –11,...
For a given A.P. a = 3.5, d = 0, then tn = _______.
If the sum of first n terms of an AP is n2, then find its 10th term.
If third term and fifth term of an A.P. are 13 and 25 respectively, find its 7th term.
Find tn if a = 20 and d = 3.
Find t5 if a = 3 and d = –3.
Decide whether 301 is term of given sequence 5, 11, 17, 23,.....
Activity :- Here, d = `square`, therefore this sequence is an A.P.
a = 5, d = `square`
Let nth term of this A.P. be 301.
tn = a + (n – 1) `square`
301 = 5 + (n – 1) × `square`
301 = 6n – 1
n = `302/6` = `square`
But n is not positive integer.
Therefore, 301 is `square` the term of sequence 5, 11, 17, 23,......
12, 16, 20, 24,...... Find 25th term of this A.P.
The nth term of an A.P. 5, 8, 11, 14,...... is 68. Find n = ?
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
