27+18+12+8+.... S8
I cant find any pattern here. Please help thanks a lot
each term is 2/3 of the precious term
27+18+12+8+16/3 + 32/9+ ...
Sir what do you mean by "precious term"
I got it now sir thanks
To find the sum of the series 27 + 18 + 12 + 8 + ... up to the 8th term, let's first look for a pattern.
We can notice that each term in the sequence is obtained by subtracting 9 from the previous term:
27 - 9 = 18
18 - 9 = 9
9 - 9 = 0
0 - 9 = -9
-9 - 9 = -18
-18 - 9 = -27
-27 - 9 = -36
As you can see, the terms decrease by 9 each time.
Now, let's list out the terms up to the 8th term:
27, 18, 12, 8, 0, -9, -18, -27.
We can observe that after the 4th term (8), the subsequent terms form a repeated pattern: -9, -18, -27.
To find the sum of the series, we need to calculate the sum of the first 4 terms, and then add the sum of the repeated pattern.
Sum of the first 4 terms:
27 + 18 + 12 + 8 = 65.
Sum of the repeated pattern:
-9 + (-18) + (-27) = -54.
Now, let's add the two sums together:
65 + (-54) = 11.
Therefore, the sum of the series 27 + 18 + 12 + 8 + ... up to the 8th term (S8) is 11.