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MCQ

Fill in the Blanks

If t_{n} denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t_{50} is ______.

#### Options

49

^{2}– 149

^{2}50

^{2}+ 149

^{2}+ 2

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#### Solution

If t_{n} denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t_{50} is **49 ^{2} + 2**.

**Explanation:**

Let S_{n} = 2 + 3 + 6 + 11 + 18 + … + t_{50}

Using method of difference, we get

S_{n} = 2 + 3 + 6 + 11 + 18 + … + t_{50}

And S_{n} = 0 + 2 + 3 + 6 + 11 + … + t_{49} + t_{50}

Subtracting equation (ii) from equation (i), we get

0 = 2 + 1 + 3 + 5 + 7 + … – t_{50} terms

⇒ t_{50} = 2 + (1 + 3 + 5 + 7 + … upto 49 terms)

⇒ t_{50} = `2 + 49/2 [2 xx 1 + (49 - 1)2]`

= `2 + 49/2 [2 + 96]`

= `2 + 49/2 xx 98`

= `2 + 49 xx 49`

= 49^{2} + 2

Concept: Concept of Series

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