Question

Arithmetic Progression.
1. What is the common difference of an A.P in which a23 – a18 = 45.
2. The sum of first ‘n ‘ terms of an A.P is given by Sn = 3n2 – n. Find the A.P.


pls answer for 15 points

Answer 1

Answer:

1) a23 - a18 = 45

a( 23 - 18 ) = 45

a * 5 = 45

therefore, a = 45/5

= 9

2) I think your qstn is not correct!!

Answer 2

Answer:

d=9, AP= 4,10, ...

Step-by-step explanation:

AP1

a23-a18= a+22d- (a+17d)= 5d

5d=45

d=9

===========

AP2

Sₙ = 3n² – n

• Sₙ= 1/2*n*(2a+d*(n-1))=
• an+1/2*nd(n-1)=
• 1/2*dn²- 1/2*dn+an=
• 1/2*dn²-1/2*(d-a)n

Sₙ = 3n² – n =  1/2*dn²-1/2*(d-a)n =>

• 1/2*d=3 => d=6

• 1/2*(d-a)=1 => d-a=2 => a=d-2=6-2=4 => a=4

AP= 4, 10, 16...