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प्रश्न
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
12, 52, 72, 73, ...
उत्तर
12, 52, 72, 73, ...
Here,
First term (a) = 12
a1 = 52
a2 = 72
Now, for the given to sequence to be an A.P,
Common difference (d) `=a_1 - a = a_2 - a_1`
Here,
`a_2 -a_1 = 5^2 - 1^2`
= 25 - 1
= 24
Also,
Since `a_1 - a = a_2 - a_1`
Hence, the given sequence is an A.P with the common difference d = 24 .
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संबंधित प्रश्न
The first three terms of an AP respectively are 3y – 1, 3y + 5 and 5y + 1. Then y equals:
(A) –3
(B) 4
(C) 5
(D) 2
Determine the 10th term from the end of the A.P. 4, 9, 14, …….., 254
Write first four terms of the A.P. when the first term a and the common differenced are given as follows:
a = -2, d = 0
Show that the sequence defined by an = 5n −7 is an A.P, find its common difference.
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
3, 6, 12, 24, ...
Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.
Priya earned ₹ 15,000 in the first month. Thereafter her salary increased by ₹ 1500 per year. Her expenses are ₹ 13,000 during the first year and the expenses increase by ₹ 900 per year. How long will it take for her to save ₹ 20,000 per month
t19 = ? for the given A.P., 9, 4, −1, −6 ........
Activity :- Here a = 9, d = `square`
tn = a + (n − 1)d
t19 = 9 + (19 − 1) `square`
= 9 + `square`
= `square`
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers
The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.
First term and common difference of an A.P. are 1 and 2 respectively; find S10.
Given: a = 1, d = 2
find S10 = ?
Sn = `n/2 [2a + (n - 1) square]`
S10 = `10/2 [2 xx 1 + (10 - 1)square]`
= `10/2[2 + 9 xx square]`
= `10/2 [2 + square]`
= `10/2 xx square = square`
