Given the geometric sequence 1,2,4,8,16,32....think a simple real-life situation which represent this sequence. Problem: A kid is saving to buy flowers as a gift for his mother. He is saving everyday for 8 days. He would like to double what he has saved for each day he has. Find his total savings. He started by putting 1 peso in his coin bank. Formula: A(n)=a1 * r ^n-1, where r is the common ratio, a1 is the first term, n is the term number, A(n) is the nth term./ Formula: S(n)=a1(1-r^n)/ 1-r. r=2/1 =2. A8= 1*2^8-1 = 1*2^7 = 1*128= 128 A8= 128 S8= 1 (1-2^8)/ 1-2= 1 (1-256)/-1 = 1(-255)/-1 = -255/-1= 255 S8= 255. Check: 32 x 2= 64. 64x2= 128. A8= 128 Check: 1+2+4+8+16+32+64+128=255 S8= 255. Answer: 255 pesos
