Question

What is the least value of n for which the sum of the series 1+4^2+4^3+... Upto n terms is greater than 341?

Answer 1

Answer:

plzz give me brainliest ans and plzzzz follow me

Answer 2

Given:

• Sum of series = $1+4^2+4^3+$ and so on.
• The sum of the series is greater than 341

To Find:

• Least value of n.

Solution:

• We can see the given series in G.P(Geometric Progression).
• We have a formula, $S_n = \frac{a(r^n-1)}{r-1}$  
• Here, r = 4, n = n+1 and a = 1
• Substitute the values in the formula,
• ⇒ $S_n = \frac{1(4^n-1)}{4-1}$
• The obtained series is greater than 341, so
• ⇒ $\frac{1(4^n-1)}{4-1}$  > 341
• ⇒ $4^n-1 > {341*3}$
• ⇒ $4^n-1> 1023$    
• ⇒ $4^n > 1024$
• The above-mentioned inequality can be written in terms of (number) raised to its power.
• ⇒   $4^n> 4^5$
• n = 5

∴ The least value of n is 5.