Q.120. Arithmetical Progression.

Question 120.
The consecutive odd numbers are grouped as follows: 1,(3,5);(7,9,11);(13,15,17.19);... Find the sum of the integers in the 20th group.

Answer 120.
There are 19 terms in 19th group.
Total no. of terms in first 19 groups = 19*20/2 = 190
190th term of AP 1, 3, 5, 7, ... is
1 + (189)*2 = 379
First term of 20th group is 381
There are 20 terms in 20th group which is an AP
381, 383, 385, ....
Sum of integers in 20th group
= (20/2) [ 2*381 + (20 -1)*2 ]
= 8000

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