Question

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Answer 1

Hi !

Sp = 3p² + 4p

sum of first term = S₁
NOTE = S₁ is the same as first term(a)

S₁ = 3(1)² + 4(1) = 3 +4 = 7

S₂ = 3(2)² + 4(2) =  20

S₃ = 3(3)² + 4(3) = 39

First term = a₁ = S₁= 7
Second term = a₂ = S₂ - S₁ = 20-7 = 13
Third term = a₃ = S₃-S₂ = 39 -20 = 19

Common difference = a₂ - a₁ = 6


The A.P is as follows :-
7,13,19 ..........

here ,
a = 7,
d = 6

an = a + (n-1)d
an = 7 + (n-1)6
an = 7 + 6n - 6
an = 6n + 1

nth term is 6n +1

Answer 2

Heya,

Given:-

Sum of p terms of an A.P is 3p² +4p

⇒ Sum of 1st term( i.e, first term of A.P) = 3(1)²+4(1)

=7

Sum of 1st two terms = 3(2)² + 4(2)

=20

⇒ 1st term of the A.P = 7 

2nd term =  S₂ - S₁

= 20-7

= 13

Therefore the A.P is 7,13.....

Common difference = 13-7

= 6

Nth term = a+ (n-1)d

= 7+(n-1)(6)

= 7 + 6n-6

=6n + 1

Hope it helps u..........