Find the Sum of n terms of Geometric Sequence a = 2, n = 10, and r =5

Steps to find sum of n terms of geometric sequence:

sum of n terms of geometric sequence formula:-

S_n = `a*(r^n-1)/(r-1)`

where:

• s_n is the sum of n terms
• a is first term
• n is total number of terms
• r is common ratio

Input values are:-

a = 2

n = 10

r = 5

Put values into formula

S₁₀ = `a*(r^n-1)/(r-1)`

S₁₀ = `2*(5^10-1)/(5-1)`

S₁₀ = 4882812.0

Follow the detailed steps listed below to find the Sum of n terms of Geometric Sequence a = 2, n = 10, and r = 5 to make your calculations faster.

• The initial step is to find out the First Term of Sequence a = 2, Common Ratio r = 5 and n = 10
• Later, substitute the given values in the Sum of n terms in G.P Formula i.e. S_n = a[(r^n-1)/(r-1)] if r > 1 and r ≠ 1 or S_n = a[(1 – rⁿ)/(1 – r)] if r < 1 and r ≠ 1
• As in the given case common ratio r is greater than 1 we will use the formula Sn = a[(r^n-1)/(r-1)] and substitute given values i.e. S₆ = 2[(5^10-1)/(5-1)]
• Simplifying further we have the Sum of n terms of Geometric Sequence S6= 4882812.0.

Example for Finding Sum of n terms of Geometric Sequence