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Thank you for your attention thank you

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u1 = 2 = 2
u2 = 4 = 2^2
u3 = 8 = 2^3
u4 = 16 = 2^4

Common ratio = Un/Un-1
un=2*2^n-1

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Arithmetic sequence:
d= common difference
U₁ = first term
Un= U₁+(n-1)d

Geometric consequence:
R = common ratio = Un/Un-1
U₁ = first term

Eg. 2,4,8,16,...
U1 = 2
U2 = 2²
U3 = 2³
U4 = 2⁴
Un = 2x2n-1
U¹ x rn-1

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Arithmetic;

Geometric;
u₁=2
u₂=2*2
u₃=2*2*2
u

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Geometric

nth term = u₁rn-1
e.g 2,4,8,16.....
u1 = 2
u2 = 4=u1x2
u3 = 8=u2x2
u4 = 16=u3x2
Common ratio is 2
2x2(n-1)

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Kaito and Zixuan

Arithmetic
nTH term:
(the difference between the consecutive terms) x n - (the difference between the consecutive terms - the first term)

Let "the difference between the consecutive terms" be A

nTH term = A x n - (A - U1)

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Arithmetic:
The difference between one term and the next term is constant.
formula→un=u₁+(n-1)d

Geometric:
A term is found by multiplying the previous term by a constant.
formula→un=u₁rn-1

n = any term number (nth term)
d = common difference
u = term
r = ratio

e.g. 2,4,8,16....
common ratio; 16/8 =2
u₁=2        2*1              =2*2⁰
u₂=4        2*2              =2*2¹
u₃=8        2*2*2          =2*2²
u₄=16      2*2*2*2      =2*23

un=2*2n-1
Hence, un=u₁*rn-1

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Arithmetic sequences: Difference between connected terms in each sequence is the same. [nth term = u1 + (n-1) * difference between each term]
Geometric sequences: A term times the same number to get the next term in each sequence.
nth term = u1*r in power of (n-1)

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Geometric
Multiply same number
form: ar(n-1)
r= common ratio
2 x 2 (n-1)

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Geometric

Common ratio:
U2 divided by U1 is 2
U3 divided by U2 is 2
U4 divided by U3 is 2

U1 = 2
U2 = 2x2
U3 = 2x2x2
U4 = 2x2x2x2

U1 = 2 times the power of 1
U2 = 2 times the power of 2

Un = 2 times the power of n-1
Un = U1r to the power of n-1