Question

Sum of n terms of an ap is 2n+3n² if first term is taken as same and the difference will be doubled then find the sum of the first n terms of an new ap

Answer 1

Here it is simply derived. Write and study.

S₁ = a = T₁ = 2+3= 5

now if we find S₂ = T₁+T₂ = 16
hence T₂= 16 –5 = 11

a+d = 11
d= 11–5 = 6

now we have find a &d for the first AP.
for second AP,
a = 5, d= 12

so S_n for second AP = (n/2)[2*5 + (n –1)* 12]
S_n = 5n + 6n² –6n
S_n = 6n² –n

Hope you understand.

Thank you :)