Question

12. A man has saved `640 during the first month, `720 in the second month and `800 in
the third month. If he continues his savings in this sequence, what will be his savings in the
25th month?

Answer 1

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….

Answer 2

Solution :

Monthwise savings of the man are

640 , 720 , 800 , .....

First term = a = a1 = 640

a2 - a1 = 720 - 640 = 80

a3 - a2 = 800 - 720 = 80

Therefore ,

a3 - a2 = a2 - a1 = 80

Given , series is in A.P

Common difference = d = 80

**************************************

nth term = an

an = a + ( n - 1 )d

**************************************

Here ,

n = 25 ,

a25 = 640 + ( 25 - 1 )× 80

= 640 + 24 × 80

= 640 + 1920

= 2560

Therefore ,

His monthly savings in the

25th month = a25 = 2560

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