Question

find the sum of first twenty five terms of AP series whose nth term is n/5+2
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Answer 1

Answer:

Step-by-step explanation:

if n=1 then

a1 = 7-3×1

= 4

if n=3 then

a2= 7-3×2

= 1

As a1 = 4 & a2 = 1

then d will be

=a2-a1

= -3

d= -3

S25 = 25/2(2×4 + (25-1)×-3)

=25/2 × -64

= 25× -32

= -800

Hence sum of 25 terms of this A.P will be (-800).

hope this helped,

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Answer 2

Given :

$n_{th}$ term of the series $a_{n} =\frac{n}{5}+2$

To find:

Sum of first 20 terms

Solution:

Since, we have the $n_{th}$ term of the series, we can calculate the series

Hence,

$a_{1} = \frac{1}{5}+2 = \frac{11}{5}$ ;

$a_{2}= \frac{2}{5}+2 = \frac{12}{5}$ ;

$a_{3}=\frac{3}{5}+2=\frac{13}{5}$ ;

and hence,

$a_{25}=\frac{25}{5}+2=7$

We can calculate the common difference by,

$d=a_{2} -a_{1}=\frac{1}{5}$ ; and

      $a_{3} -a_{2}=\frac{1}{5}$

Therefore, we have,

$a=\frac{11}{5}$  $;$  $d=\frac{1}{5}$  $;$  $n=25$

Hence, the sum of first 20 terms $=\frac{n}{2}(2a+(n-1)d)$

                                                      $= \frac{25}{2}(2(\frac{11}{5}) +(25-1)\frac{1}{5} )$

                                                      $= \frac{25}{2} (\frac{46}{5} )$

Sum of first 25 terms in the AP $=115$

Final answer;

Hence, the sum of first 25 terms off the A.P. is 115.