Advertisements
Advertisements
प्रश्न
Find the number of terms in the following A.P.: 7, 13, 19, ..., 205.
How many terms are there in the A.P.?
7, 13, 19, ..., 205.
उत्तर
For this A.P.,
a = 7
d = a2 − a1 = 13 − 7 = 6
Let there are n terms in this A.P.
an = 205
We know that
an = a + (n - 1) (d)
⇒ 205 = 7 + (n - 1) (6)
⇒ 205 = 7 + 6n - 6
⇒ 6n = 205 + 6 - 7
⇒ 6n = 204
⇒ n = `204/6`
⇒ n = 34
Thus, the required number of terms is 34.
संबंधित प्रश्न
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Which term of the A.P. 8, 14, 20, 26, ... will be 72 more than its 41st term?
Write the first five terms of the following sequence whose nth term is:
an = 2n2 − 3n + 1
Find the next five terms of the following sequences given by:
a1 = 4, an = 4an−1 + 3, n > 1.
Which term of the A.P. 4, 9, 14, ... is 254?
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
How many numbers of two digit are divisible by 3?
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.
Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
(i) 9, 15, 21, 27,…………
The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.
The sum of first n terms of an AP is 3n2 + 4n. Find the 25th term of this AP ?
The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term ?
The 11th term of the AP: `-5, (-5)/2, 0, 5/2, ...` is ______.
Write the first three terms of the APs when a and d are as given below:
a = –5, d = –3
Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.
What is the common difference of an AP in which a18 – a14 = 32?
If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| 3.5 | 0 | 105 | ______ |
Which term of the A.P. `-11/2, -3, -1/2`.... is `49/2`?
