Question

Find Sn of the following arithmetico -

geometric sequences

i) 2, 4x, 6x2

, 8x3

, 10x4

, …see​

Answer 1

Step-by-step explanation:

Given Find Sn of the following arithmetico -geometric sequences

• Now the given sequence is 2,4x,6x^2,8x^3,10x^4
• Now Sn = 2 + 4x + 6x^2 + 8x^3 + 10x^4 ---------------1
• Multiply by x on both sides we get
• So x.Sn = 2x + 4x^2 + 6x^3 + 8x^4 + 10x^5 -------------2
• Subtracting equation 1 and 2 we have
• So Sn – x Sn = 2 + 2x + 2x^2 + 2x^3 + 2x^4
• Now Sn(1 – x) = 2 (1 + x + x^2 + x^3 +………..)
• So we have sum of infinite terms in G.P will be
• Sn = a / 1 – r (r < 1)
• Now 1 + x + x^2 will be a G.P
• So r = a2 / a1
•       = x
• So Sn(1 – x) = 2 x 1 / 1 – x
• Or Sn = 2 / (1 – x)^2

Reference link will be

https://brainly.in/question/11842560