Question

the front row of the stadium has 25 seats. each of the other rows has 2 more seats than the row in front of it. how many seats are there altogether in the first 20 rows?

Answer 1

Use Sum Formula of Arithmetic progression @neer2890

Answer 2

what is the formula?

Answer 3

Sir first you try

Answer 4

its\[s _{n}=\frac{ n(a _{1}+a _{2}) }{ 2 }\]

Answer 5

so in 1st row , 25 seats are there.
in 2nd row, 25+2=27 seats are there.
in 3rd row, 29 seats are there.
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for 20th row use formula
\[a _{n}=a+(n-1)d\]
where an is nth term
a= 1st term
d is common difference between any two terms

Answer 6

but its asking how many there are altogether in the first 20 rows

Answer 7

so\[a _{20}= 25+(20-1)2=25+19*2=63\]
now the question becomes
25+27+29+.............+63
so use \[S _{n}=\frac{ n }{ 2 }[a+l]\]
where, Sn is sum of n terms
a is 1st term
and l is last term.

Answer 8

ok tten what about this problem:
the first term of a sequence is 1, and the 5th term is 47. if the difference between consecutive terms is constant, what is the 2nd term?

Answer 9

use the same formula
\[a _{n}=a+(n-1)d\]

Answer 10

what would be d though?

Answer 11

\[a _{5}=a+(5-1)d\]
find d
and
use
\[a _{2}=a+(2-1)d\]
to find a2

Answer 12

but how do i find d?

Answer 13

you know a5=47 and a=1
just put their values
in a5=a+(5-1)d
and find d.

Answer 14

\[S _{n}=\frac{ n }{ 2 }\left\{ 2a+\left( n-1 \right) d \right\}\]

Answer 15

a=25
d=2
n=20