Addition Tricks (5)

Algebra Level 2

Consider a geometric progression with common ratio 4. If the sum of the first 6 terms is 6825, what is the initial term?

4 6 3 5

2 solutions

Hung Woei Neoh
Apr 23, 2016

Given that $r=4$

$S_6 = 6825\\ \dfrac{a(4^6-1)}{4-1} =6825\\ \dfrac{a(4096-1)}{3} = 6825\\ a=\dfrac{6825(3)}{4095}\\ a=\boxed{5}$

Sparsh Sarode
Apr 22, 2016

Sn=a(r^n - 1)/(r - 1), S6=a(4^6 - 1)/(4 - 1) = 6825, a(4096 - 1)/3 = 6825, a(4095)/3 = 6825, a(1365) = 6825, a = 6825/1365, a = 5