Advertisements
Advertisements
Questions
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.
Solution
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.
APPEARS IN
RELATED QUESTIONS
Find the number of terms in the following A.P.
`18,15 1/2, 13`, ..., – 47
Write the first five terms of the following sequences whose nth terms are:
`a_n = (2n - 3)/6`
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.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A.P.
Find the 10th term from the end of the A.P. 8, 10, 12, ..., 126.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.
Which term of the A.P. 3, 15, 27, 39, ... will be 120 more than its 21st term?
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
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 the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P ?
If the common difference of an AP is 5, then what is a18 – a13?
If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.
The 10th term from the end of the A.P. 4, 9,14, …, 254 is ______.
The next term of the AP `sqrt18, sqrt50, sqrt98, ....` is ______.
Write the first three terms of the APs when a and d are as given below:
a = `1/2`, d = `-1/6`
The first four terms of an AP, whose first term is –2 and the common difference is –2, are ______.
The 4th term from the end of the AP: –11, –8, –5, ..., 49 is ______.
In an A.P., the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, then find its middle term.
Which term of the A.P. : 65, 61, 57, 53, .............. is the first negative term?
