Question

The sum of the first 20 terms common between the series
3+7+ 11 + 15 + .... and 1 +6+ 11 + 16 + ..... is
(2014/Online Set-2)
(a) 4000
(b)4020
(c) 4200
(d) 4220​

Answer 1

Answer:

option (b)

Step-by-step explanation:

the series are:

3,7,11,15,19,23,27,31...........

1,6,11,16,21,26,31........

common terms are 11,31....

here a=11,d=20

so S20=20/2(2*11+(19*20)

=10*(22+380)

=10*402

=4020

option (b)

Answer 2

Answer:

$S_2_0\;=\;4020$

Step-by-step explanation:

Given $n = 20$ and $S_2_0=?$

Series $(1)\rightarrow$ 3 , 7 , 11 , 15 , 19 , 23 , 27 , 31 , 35 , 39 , 43 , 47 , 51 , 55 , 59 , .. 71

Series $(2)\rightarrow$ 1 , 6 , 11 , 16 , 21 , 26 , 26 , 31 , 36 , 41 , 46 , 51 , 56 , 61 , 66 , 71 .

The common terms between both the sequences :

11 , 31 , 51 , 71

Now, $S_n\;=\;\frac{n}{2}[2a+(n-1)d]$

Here, n is 20, first term is 11 and common difference is 20.

So, $S_2_0\;=\;\frac{20}{2}[2\times11+(20-1)20]$

∴ $S_2_0\;=\;4020$