Question

Find the sum of 2,6,10.........50th term

Answer 1

Given numbers are AS ( Sequence of AP ) therefore there will be a common difference in all the terms, to get that common difference we have to subtract second term from third term , first term from second , the result will be same if it is  AS.

Common difference : 10 - 6 = 6 - 2 = 4

Therefore the common difference( d ) in all terms is 4.

Starting number of any series is it's first term, therefore first term( a ) = 2

Last term = a + ( l - 1 )d

$a_{l} = a + ( l - 1 )d$

$a_{50} = 2 + ( 50 - 1 )4$

$a_{50} = 2 + (49)4 \\ \\a_{50} = 2 + 196\\\\a_{50} = 198$

Therefore, last or 50th term is 200.

We know that in AP sum of n terms is $\dfrac{n}{2} [\: a + l\:]$

Hence,

sum of 50 terms = $\dfrac{50}{2}[2+198]$

sum of 50 terms = 25( 200 )  

sum of 50 terms = 5000

Hence, sum of 50 terms is 5000.

Answer 2

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