Find the sum of the first 27 terms of the following sequence:
10, 18, 26 . . .
For an AS
Sum(n) = (n/2)(2a + d(n-1))
in your case
Sum(27) = (27/2)(20 + 26(8) )
= ...
To find the sum of the first 27 terms of the given sequence, we need to find the pattern and use the formula for the sum of an arithmetic sequence.
The given sequence has a common difference of 8, as each term is obtained by adding 8 to the previous term.
To find the nth term of an arithmetic sequence, you can use the formula:
nth term = first term + (n - 1) * common difference
Using this formula, we can find the 27th term of the sequence:
27th term = 10 + (27 - 1) * 8
= 10 + 26 * 8
= 10 + 208
= 218
So, the 27th term of the sequence is 218.
Now, to find the sum of the first 27 terms of an arithmetic sequence, we use the formula for the sum:
Sum = (n / 2) * (first term + last term)
Using this formula, we can find the sum of the first 27 terms:
Sum = (27 / 2) * (10 + 218)
= 13.5 * 228
= 3084
Therefore, the sum of the first 27 terms of the given sequence is 3084.