Advertisements
Advertisements
Question
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Advertisements
Solution
5, 1, –3, –7, ...
Here, a = t1 = 5, t2 = 1, t3 = −3, ...
The first term (a) = 5
d = t2 − t1
= 1 − 5
= −4
RELATED QUESTIONS
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
The sum of the first n terms of an AP is `((3n^2)/2 + (5n)/2)`. Find its nth term and the 25th term.
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Q.14
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
Which expression gives the sum of the first n natural numbers \[1 + 2 + \cdots + n\]?
