Question

Find the sum of first 50 tcrms of A.P. 14, 16, 18,...​

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The sum of first 50 terms of A.P.

14 , 16 , 18 , . . .

CONCEPT TO BE IMPLEMENTED

Sum of first n terms of an arithmetic progression

$\displaystyle \sf = \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

Where First term = a

Common Difference = d

Number of terms = n

EVALUATION

Here the given arithmetic progression is

14 , 16 , 18 , . . .

First term = a = 14

Common Difference = d = 16 - 14 = 2

Number of terms = n = 50

Hence the required sum

$\displaystyle \sf = \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

$\displaystyle \sf = \frac{50}{2} \times \bigg[(2 \times 14) + (50 - 1) \times 2 \bigg]$

$\displaystyle \sf = \frac{50}{2} \times \bigg[28 + (49 \times 2) \bigg]$

$\displaystyle \sf = 25 \times \bigg[28 + 98 \bigg]$

$\displaystyle \sf = 25 \times 126$

$\displaystyle \sf =3150$

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