Advertisements
Advertisements
Question
Which of the following sequences are A.P.? If they are A.P. find the common difference.
`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2, ...`
Solution
t2 − t1 = `3 + sqrt2 - 3 = sqrt2`
t3 − t2 = `3 + 2sqrt2 - (3 + sqrt2)`
= `3 + 2sqrt2 - 3 - sqrt2`
= `sqrt2`
t4 − t3 = `3 + 3sqrt2 - (3 + 2sqrt2)`
= `3 + 3sqrt2 - 3 - 2sqrt2`
= `sqrt2`
∵ The difference between consecutive terms are same.
∴ Given sequence is an A.P.
Common difference (d) = `sqrt2`
APPEARS IN
RELATED QUESTIONS
In an AP, the first term is 2, the last term is 29 and the sum of all the terms is 155. Find the common difference.
In an AP, the first term is 22, nth terms is -11 and sum of first n terms is 66. Find the n and hence find the4 common difference.
The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in the ratio 1:5, find the AP.
The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms.
An AP 8, 10, 12, … has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.
Find the sum of all three digit natural numbers, which are multiples of 7 ?
Is the following sequences are A.P.? If is A.P. find the common difference.
0.3, 0.33, 0.333,...
On 1st Jan 2016, Sanika decides to save Rs 10, Rs 11 on second day, Rs 12 on third day. If she decides to save like this, then on 31st Dec 2016 what would be her total saving?
Find x if x + y = 5, and x - y = 7
The estimated tax on the income of Shreemati Hinduja is Rs. 8000. How much education cess has she to pay at 3% ?
Find the class-mark of 80-90.
A = {1, 2, 3,4, 5}, B = {5, 6, 7} write AUB .
Find the 19th term of the A.P. 7, 13, 19, 25, ............ .
Amit saves a certain amount every month in a specific way. In the first month, he saves Rs. 200, in the second month Rs. 250, in the third month Rs.300 and so on. How much will be his total savings in 17 months?
Find the sum of all numbers from 50 to 350 which are divisible by 4. Also, find the 15th term.
Find S2 for the A.P. 3,5,7,9,......
Find out the ratio of 1 mm to 1 cm.
Complete the following activity to find the number of natural numbers between 1 and 171, which are divisible by 5:
Activity :
