A man saved 16500/- in ten years . in each year after the first he saved 100/- more then he did in the preceding year. How much did he saved in the first year?

Given: A man saved 16500/- in ten years


To find: His saving in the first year


Let he saved Rs. x in the first year


Since each year after the first he saved 100/- more then he did in the preceding year


So,


A.P will be x, 100 + x, 200 + x………………..


where x is first term and


common difference, d = 100 + x – x = 100


We know,


Sn is the sum of n terms of an A.P


Formula used:



where a is first term, d is common difference and n is number of terms in an A.P.


According to the question:


Sn = 16500 and n = 10


Therefore,



16500 = 5{2x + 9(100)}


16500 = 5(2x + 900)


16500 = 10x + 4500


-10x = 4500 – 16500


–10x = –12000



x = 1200


Hence, his saving in first year is 1200


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