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2 months, 3 weeks ago

If the sum of the first 15 terms of the series 3+7+14+24+37+.......is 15K, then k is equal to :

- Option 1)
126

- Option 2)
122

- Option 3)
81

- Option 4)
119

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Summation of series of natural numbers -

- wherein

Sum of first n natural numbers

and

Summation of series of natural numbers -

- wherein

Sum of squares of first n natural numbers

3+7+14+24+37 ----------15K

Let T_{n}=an^{2}+bn+c because difference is in A.P: [4,7,10,13-----------------]

at n=1 ------(i)

n=2 -------(ii)

n=3 -------(iii)

(ii)-(i) -------- (iv)

(iii)-(ii) -------- (v)

(v)-(iv)

from (i)

from (ii)

Put n=15

Option 1)

126

This option is incorrect

**Option 2)**

**122**

**This option is correct**

Option 3)

81

This option is incorrect

Option 4)

119

This option is incorrect

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