A. There are many ways of adding a geometric sequence:
1. If you can not see all the digits then:
[(first number) + (last number)] x number of terms
2
*Note: This way works for any sequence. If you like you can use this method for step 2 and step 3.
Ex [1] 4 + 8 + 12 + ... + 48 =_________.
a) Notice the number of terms is 12.
b) (4 + 48) x 12 / 2 = 52 x 6 = 312.
c) The answer is 312.
Ex [2] 7 + 13 + 19 + ... + 47 =_________.
a) Notice the number of terms is 11. (*All you have to do is subtract 3 and divide by 4.)
b) (47 + 7) x 11 / 2 = 27 x 11 = 297. See Multiplying by 11.
c) The answer is 297.
2. If you can see all the digits and there is an odd number then:
Multiply the middle digit by the number of terms
Ex [3] 15 + 25 + 35 + 45 + 55 =_________.
a) The middle digit is 35 and there are 5 numbers.
b) 35 x 5 is 175.
c) The answer is 175.
Ex [4] 7 + 9 + 11 + 13 + 15 + 17 + 19=_________.
a) The middle digit is 13 and there are 7 numbers.
b) 13 x 7 = 91.
c) The answer is 91.
3. If you can see all the digits and there is an even number then:
Add the middle 2 digits and multiply by half the number of terms
Ex [5] 6 + 12 + 18 + 24 + 30 + 36 =_________.
a) (18 + 24) x 3 = 42 x 3 = 126.
b) The answer is 126.
Ex [6] 9 + 12 + 15 + 18 + 21 + 24 =_________.
a) (18 + 15) x 3 = 33 x 3 = 99.
b) The answer is 99.