Question

Find the sum of the fillowing 1.50,46,42,---------to 10 term 2.1,3,5,7,------------- to 21 term

Answer 1

Hey ,

Solution ☺☺ ......
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1 .
The given A.P is 50 , 46, 42.........

Here,
a = 50 and d = ( 46 - 50 ) = -4

Using the formula ―

$sn = \frac{n}{2} .(2a + (n - 1)d) \\ \\ s10 = \frac{10}{2} (2 \times 50 + (10 - 9) \times ( - 4)) \\ \\ s10 = 5(100 + 9 \times ( - 4)) \\ \\ s10 = 5(100 - 36) = 64 \\ \\ s10 = 5 \times 64 \\ \\ s10 = 320$

Hence , the required sum is 320.

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2.

The given A.P is 1, 3 , 5, 7 .......

Here ,
a = 1 and d = ( 3- 1)= 2

using formula ―

we have -
$sn = \frac{n}{2} .(2a + (n - 1)d) \\ \\ s21 = \frac{21}{2} (2 \times1 + (21 - 1) \times 2 \\ \\ s21 = \frac{21}{2} (2 + 20 \times 2) \\ \\ s21 = \frac{21}{2} ( 2 + 40) \\ \\ s21 = \frac{21}{2} \times 42 \\ \\ s21 = 21 \times 21 \\ \\ s21 = 441$
Hence , the required sum is 441 .

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Hope it's helps you.
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