An arithmetic progression is a list of numbers a1, a2, a3 ………….. an in which each term is obtained by adding a fixed number to the preceding term except the first term.
This fixed number is called the common difference( d ) of the AP. Common difference of an AP will be the difference between any two consecutive terms.
an= an-1+d ………
Each of the numbers in the list is called a term .
Method to find the common difference :
d = a2 - a1 or a3 - a2 or a4 - a3...
General form of an AP.:
a, a+d, a+2d, a+3d…….
Here a is the first term and d is common difference.
General term or nth term of A.P
The general term or nth term of A.P is given by an or tn = a + (n – 1)d, where a = a1 is the first term, d is the common difference and n is the number of term.
A man saved in the first month,in the second month ,in the third month… are 640, 720, 800 .. which forms a sequence(AP).
Here, a1 or t1 = 640 , a2 or t2= 720, a3 or t3 = 800
d = t2 – t1
d= 720- 640
tn = a + (n-1) d
t25 = 640 + (25 - 1) 80
t25 = 640 + 24 (80)
t25= 640 + 1920
t25 = 2560
Hence, his Saving will be 2560 in the 25th month.
HOPE THIS WILL HELP YOU….
Monthwise savings of the man are
640 , 720 , 800 ,
First term = a = a1 = 640
a2 - a1 = 720 - 640 = 80
a3 - a2 = 800 - 720 = 80
a3 - a2 = a2 - a1 = 80
Given , series is in A.P
Common difference = d = 80
nth term = an
an = a + ( n - 1 )d
n = 25 ,
a25 = 640 + ( 25 - 1 )× 80
= 640 + 24 × 80
= 640 + 1920
His monthly savings in the
25th month = a25 = 2560
your answer for value of x is 4
given it becomes rs 7396 in 2 years
it is also given that principal rs x becomes rs 7950.70 in 3 years.
divide (2) with (1), we get
∴ y = 7.5
thus the rate of interest is 7.5%.