Question

If the sum of first n terms of an AP is 4n-n^2 , what is the first term? what is the sum of first two terms? what is the second term? find the 3rd 10th and nth term?​

Answer 1

Answer:

See below

Step-by-step explanation:

If the sum of first n terms of an AP is 4n-n^2 , what is the first term? what is the sum of first two terms? what is the second term? find the 3rd 10th and nth term?​

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• S₁= a₁= 4*1-1^2= 3
• S₂= a₁+ a₁+d= 4*2-2^2= 8-4=4

• 6+d=4 => d= 4-6= -2
• a₂=a₁+d= 3-2= 1
• a₃= a₁+2d= 3-2*2= -1
• a₁₀= a₁+9d= 3-9*2= -15
• aₙ= a₁+(n-1)d= 3-2(n-1)= 3-2n+2= 5-2n

First term = 3

The sum of first 2 terms = 4

Second term = 1

3rd term = -1

10th term = -15

nth term = 5-2n

Answer 2

Answer:

hi

hope this helps you!

Step-by-step explanation:

Sn=4n-n'2

S1=4-16

=-12

S2=8-16=-8

S3=12-16=-4

so A1=-12

A2=S2-S1=4

A3=S3-S2=20

A10=a+ (n-1)d

-12+(9)16=132

An=a+(n-1)d

=-12+(n-1)16

=-12+16n-16

=16n-28

thereforeAn = 16n+28