Question
Question: If S<sub>1</sub> = {1}, S<sub>2</sub> = {3, 5}, S<sub>3</sub> = {7, 9, 11}, S<sub>4</sub> = {13, 15,...
If S1 = {1}, S2 = {3, 5}, S3 = {7, 9, 11}, S4 = {13, 15, 17, 19} and so on, then the sum of all the numbers in S20 is
A
10000
B
10,100
C
8100
D
8000
Answer
8000
Explanation
Solution
First entry of each set form a series
1, 3, 7, 13, 21,………
Let tn be the nth term of the series
Sn = 1 + 3 + 7 + 13 + 21 + ………. + tn
Sn = 1 + 3 + 7 + 13 + ………. + tn–1 + tn
0 = 1 + 2 + 4 + 6 + 8 + …… + (tn – tn–1) – tn
tn = 1 + 2n–1 [4 + (n – 2) .2]
= 1 + (n – 1). n = n2 – n + 1
tn = n2 – n + 1
\first term in S20 is = 400 – 20 + 1 = 381
Sum of the numbers in
S20 = 220 (762 + 19 × 2) = 8000