12. a man has saved `640 during the first month, `720 in the second month and `800 in
the month. if he continues savings in sequence, what will be savings in the
25th month?

AP ( Arithmetic progression).
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.

a2= a1+d
a3= a2+d
a4= a3+d
……..
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.

SOLUTION :
Given -
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
d= 80

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….

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