Question -
Answer -
Given: A mansaved ₹16500 in ten years
Let ₹ x be his savingsin the first year
His savings increasedby ₹ 100 every year.
So,
A.P will be x, 100 +x, 200 + x………………..
Where, x is first termand
Common difference, d =100 + x – x = 100
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 =16500 and n = 10
S10 =10/2 [2x + (10 – 1)100]
16500 = 5{2x + 9(100)}
16500 = 5(2x + 900)
16500 = 10x + 4500
-10x = 4500 – 16500
–10x = –12000
x = 12000/10
= 1200
Hence, his saving inthe first year is ₹ 1200.