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Some Special Series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSome Special Series1 Mark
Question
Write the $50^{th}$ term of the series $2 + 3 + 6 + 11 + 18 + ....$
✓

Answer

We have,
$a_1 = 2,$
$a_2 = 3 = 2 + 1,$
$a_3 = 6 = 2 + 1 + 3,$
$a_4 = 11 = 2 + 1 + 3 + 5,$
$.............................$
$.............................$
$..............................$
$a_{50} = 2 + 1 + 3 + 5 + .... (50$ terms$)$
$=2+\frac{49}{2}\big[2\times1+(49-1)\times2\big] ($As, the terms apart $2$ are in A.P. with $a = 1$ and $d = 2)$
$=2+\frac{49}{2}(2+48\times2)$
$=2+\frac{49}{2}\times98$
$=2+49^2$
$=2+2401$
$=2403$
So, the $50^{th}$ term of the given series is $2403$

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