Question

5. The first three terms of a geometric sequence are 2k + 2,5% + 1, and 10k + 2, k > 0. Determine the sum of the first 10 terms of the sequence. (5 marks)

Answer 1

Given that First three term of a Geometric Sequence are QK tag 5K+1 and lokt 2 ko 1 As we know general form of GS first three tenm is a, ar and 9 therefor a=2ktQ r ara - šlo a ar lokta 2 (5K+1) 5KtI r l] 5 KHI 5K+1 2x+2 5kti =) r= akta there for rad and by using 5K+1 2 (2K+2) = 4K + 2+2 5K+1 TK=3

we have r=2 therefor So first k=3 9 10-term OP sequence are aq ara are, 9 lar for a=8 r=2 9 8 16,38,864, 128, 256, 512, 10249 2048, 4096 As r=2> Hence Sum of first N-term will be a crna Sn = rol 10 Sio = 8 (8-1) = 8x1024 2-1 8192