How Many Terms of the Geometric Progression 1 + 4 + 16 + 64 + …….. Must Be Added to Get Sum Equal to 5461? - Mathematics

Sum

How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?

Solution

Given G.P. : 1 + 4 + 16 + 64 +...........
Here,
first term, a = 1
common ratio, r = 4/1=4 (r > 1)
Let the number of terms to be added = n
Then, Sn = 5461

=>(a(r^n-1))/(r-1)=5461

=> (1(4^"th"-1))/(4-1)=5461

=>(4^"th"-1)/3=5461

⇒ 4th - 1 = 16383

⇒ 4th = 16384

⇒ n = 7

Hence, required number of terms = 7

Concept: Simple Applications - Geometric Progression
Is there an error in this question or solution?

APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 2 | Page 161