Democracy is a form of government in which the rulers are elected by the people. This means that:
A. Rulers elected by the people take all the major decisions
B. it is now easier for women to legally wage struggle for their rights
C. Leaders keep changing in a democracy
D. Democracy leads to delays since so many people have to be consulted
Answers
Question:-
If the sum of 'N' terms of an AP is 3n² - 2n. Find the nth term of that AP.
Solution:-
\tt\implies \: { 3n }^{ 2 } - 2n - [ 3{ ( n - 1 ) }^{ 2 } - 2( n - 1 ) ]⟹3n
2
−2n−[3(n−1)
2
−2(n−1)]
\tt\implies \: { 3n }^{ 2 } - 2n - [ 3({ n }^{ 2 } + 1 - 2n ) - 2( n - 1 ) ]⟹3n
2
−2n−[3(n
2
+1−2n)−2(n−1)]
\tt\implies \: { 3n }^{ 2 } - 2n - [ { 3n }^{ 2 } + 3 - 6n - 2n + 2 ]⟹3n
2
−2n−[3n
2
+3−6n−2n+2]
\tt\implies \: { 3n }^{ 2 } - 2n - [ { 3n }^{ 2 } - 8n + 5 ]⟹3n
2
−2n−[3n
2
−8n+5]
\tt\implies \: { 3n }^{ 2 } - 2n - { 3n }^{ 2 } + 8n - 5⟹3n
2
−2n−3n
2
+8n−5
\tt\implies \: 6n - 5⟹6n−5
Now ,
Take n = 1 in equation , then we get:-
\tt\implies \: 6( 1 ) - 5⟹6(1)−5
\tt\implies \: 6 - 5⟹6−5
\tt\implies \: 1⟹1
Take n = 2 in equation , then we get:-
\tt\implies \: 6( 2 ) - 5⟹6(2)−5
\tt\implies \: 12 - 5⟹12−5
\tt\implies \: 7⟹7
Series = 1 , 7 , 13 , 19
Common difference = b - a
Common difference = 7 - 1
Common difference = 6
Arithmetic Progression formula
Tn = a + ( n - 1 )d
Tn = 1 + ( n - 1 )6
Tn = 1 + 6n - 6
Tn = 6n - 5