Question -
Answer -
Given:
First year savings is₹ 32
Second year savings is₹ 36
In this process heincreases his savings by ₹ 4 every year
Then,
A.P. will be 32, 36,40,………
Where, 32 is firstterm and common difference, d = 36 – 32 = 4
We know, Sn isthe sum of n terms of an A.P
By using the formula,
Sn =n/2 [2a + (n – 1)d]
where, a is firstterm, d is common difference and n is number of terms in an A.P.
Given:
Sn =200, a = 32, d = 4
Sn =n/2 [2a + (n – 1)d]
200 = n/2 [2(32) +(n-1)4]
200 = n/2 [64 + 4n –4]
400 = n [60 + 4n]
400 = 4n [15 + n]
400/4 = n [15 + n]
100 = 15n + n2
n2 +15n – 100 = 0
n2 +20n – 5n – 100 = 0
n (n + 20) – 5 (n +20) = 0
(n + 20) – 5 (n + 20)= 0
(n + 20) (n – 5) = 0
n = -20 or 5
n = 5 [Since, n is apositive integer]
Hence, the manrequires 5 days to save ₹ 200