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Question
If tn denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t50 is ______.
Options
492 – 1
492
502 + 1
492 + 2
Solution
If tn denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t50 is 492 + 2.
Explanation:
Let Sn = 2 + 3 + 6 + 11 + 18 + … + t50
Using method of difference, we get
Sn = 2 + 3 + 6 + 11 + 18 + … + t50
And Sn = 0 + 2 + 3 + 6 + 11 + … + t49 + t50
Subtracting equation (ii) from equation (i), we get
0 = 2 + 1 + 3 + 5 + 7 + … – t50 terms
⇒ t50 = 2 + (1 + 3 + 5 + 7 + … upto 49 terms)
⇒ t50 = `2 + 49/2 [2 xx 1 + (49 - 1)2]`
= `2 + 49/2 [2 + 96]`
= `2 + 49/2 xx 98`
= `2 + 49 xx 49`
= 492 + 2
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