Sequence And Series

Question 1

AP

Tn

Sn

Answer 1

Tn= a+(n-1)d

Sn= n/2 [2a(n-1)d]
Or
n/2 (a+l)

Question 2

GP

Tn

Sn

Answer 2

Tn= ar^(n-1)

Sn= a(r^n -1)/r-1 r>1

Sn= a( 1-r^n) / 1-r r<=1

Question 3

Assumption terms

AP

Answer 3

3•••••• (a-d) a (a+d)
4•••••• (a-3d) (a-d) (a+d) (a+3d)
5••••••(a-2d) (a-d) a (a+d) (a+2d)

Question 4

GP

Assumption terms

Answer 4

3 terms•••••••• a/r, a, ar

4 terms•••••••• a/r^3 a/r ar a ar^3

5 terms•••••••• a/r^2 a/r a ar ar^2

Question 5

AM GM HM

Answer 5

Terms AM. GM. HM

2. a+b/2. √ab. 2ab/ a+b
3. a+b+c/3. 3√abc. 3abc/a+b+c
   n. a+b+c…n/n. (abc…n)^1/n. 1/wtevr AP

AM>=GM>=HM

Question 6

Sum of frst n odd numbers

Answer 6

n^2

Question 7

Sum of first n even numbers

Answer 7

n(n+1)

Question 8

£n

Answer 8

n(n+1)/2

Question 9

£n^2

Answer 9

n(n+1)(2n+1)/6

Question 10

£n3

Answer 10

[n(n+1)/2]^2

Question 11

Infinite GP

Answer 11

S°° =a/1-r