Question

If a = 1, r=2 find Sn for the G.P.
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Answer 1

Step-by-step explanation:

sn= a(rn-1)/r-1

sn=1×2ñ-1/1

sn= 2 raise to n-1

Answer 2

Sₙ =  2ⁿ - 1  for GP where a = 1 and r = 2

Given:

• GP ( geometric  Progression)
• a = 1  ( first term)
• r = 2  ( common ratio)

To Find:

• Sₙ   ( Sum of first n terms)

Solution:

Geometric sequence

A sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.

a , ar , ar² , ... , arⁿ⁻¹

The nth term of a geometric sequence with the first term a and the common ratio r is given by:   aₙ = arⁿ⁻¹

Sum is given by  Sₙ = a(rⁿ - 1)/(r - 1)

Sum of  infinite series is given by  a/(1 - r)   where -1 < r < 1  

Geometric Series

The sum of the terms of a geometric sequence is called a geometric series.

Step 1:

Use the formula:

Sₙ = a(rⁿ - 1)/(r - 1)

Step 2:

Substitute a = 1  and r = 2  and simplify

Sₙ = 1(2ⁿ - 1)/(2 - 1)

Sₙ = 1(2ⁿ - 1)/1

Sₙ =  2ⁿ - 1

Conclusion:

Sₙ =  2ⁿ - 1  for GP where a = 1 and r = 2