Question
Show that the sequence defined by $a_n = 5n - 7$ is an A.P, find its common difference.
✓
Answer
In the given problem, we need to show that the given sequence is an A.P. and then find its common difference.
Here,
$a_n = 5n - 7$
Now, to show that it is an A.P, Will find its few terms by substituting $n = 1, 2, 3, 4, 5$
So,
Substituting $n = 1$, we get
$a_1 = 5(1) - 7$
$a_1 = -2$
Subsituting $n = 2$, we get
$a_2 = 5(2) - 7$
$a_2 = 3$
Subsituting $n = 3$, we get
$a_3 = 5(3) - 7$
$a_3 = 8$
Subsituting $n = 4$, we get
$a_4 = 5(4) - 7$
$a_4 = 13$
Subsituting $n = 5$, we get
$a_5 = 5(5) - 7$
$a_5 = 18$
Further, for the given sequence to be an A.P,
We find the common difference (d)
$a = a_2 - a_1 = a_3 - a_2$
thus,
$a_2 - a_1 = 3 - (-2) = 5$
Since $a_2 - a_1 = a_3 - a_2$
Hence, the given sequence is an A.P, and its common difference is $d = 5.$
Here,
$a_n = 5n - 7$
Now, to show that it is an A.P, Will find its few terms by substituting $n = 1, 2, 3, 4, 5$
So,
Substituting $n = 1$, we get
$a_1 = 5(1) - 7$
$a_1 = -2$
Subsituting $n = 2$, we get
$a_2 = 5(2) - 7$
$a_2 = 3$
Subsituting $n = 3$, we get
$a_3 = 5(3) - 7$
$a_3 = 8$
Subsituting $n = 4$, we get
$a_4 = 5(4) - 7$
$a_4 = 13$
Subsituting $n = 5$, we get
$a_5 = 5(5) - 7$
$a_5 = 18$
Further, for the given sequence to be an A.P,
We find the common difference (d)
$a = a_2 - a_1 = a_3 - a_2$
thus,
$a_2 - a_1 = 3 - (-2) = 5$
Since $a_2 - a_1 = a_3 - a_2$
Hence, the given sequence is an A.P, and its common difference is $d = 5.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of the squares of two consecutive multiples of $7$ is $1225$. Find the multiples.
→Find the mode of the following frequency distribution:
→|
Marks
|
$10-20$
|
$20-30$
|
$30-40$
|
$40-50$
|
$50-60$
|
|
Frequency
|
$12$
|
$35$
|
$45$
|
$25$
|
$13$
|
Find the mean of each of the following frequency distributions:
|
Class interval
|
0-8
|
8-16 | 16-24 | 24-32 | 32-40 |
|
Frequency
|
5 | 6 | 4 | 3 | 2 |
A box contains cards numbered 3, 5, 7, 9, ..., 35, 37. A card is drawn at random from the box. Find the probability that the number on the card is a prime number.
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
A triangle PQR is drawn to circumscribe a circle of radius 8cm such that the segments QT and TR, into which QR is divided by the point of contact T, are of lengths 14cm and 16cm respectively. If area of $\triangle\text{PQR}$ is $336cm^2$, find the sides PQ and PR.
→A businessman bought some items for ₹ 600. Keeping 10 items for himself he sold the remaining items at a profit of ₹ 5 per item. From the amount received in this deal he could buy 15 more items. Find the original price of each item.
For the given trading chain prepare the tax invoice I, II, III. GST at the rate of 12% was charged for the article supplied.
(1) Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government.
(2) At the end what amount is paid by the consumer?
(3) Write which of the invoices issued are B2B and B2C?
(1) Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government.
(2) At the end what amount is paid by the consumer?
(3) Write which of the invoices issued are B2B and B2C?
Determine the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.
Construct a triangle similar to $\triangle\text{ABC}$ in which AB = 4.6cm, BC = 5.1cm, $\angle\text{A}=60^\circ$ with scale factor 4 : 5.
→