The sum of the first 15 terms of an arithmetic series is 1290. The sum of the first 16 terms is 1464.
Find t16? Find S20
clearly T16 = 1464-1290 = 174
S16 = 16/2 (a+174) = 1464
a = 9
T16 = 9+15d = 174
d=11
S20 = 20/2 (2*9+11*19) = 2270
To find t16, we need to determine the common difference (d) of the arithmetic series.
We can find the common difference by subtracting the sum of the first 15 terms from the sum of the first 16 terms.
d = sum of the first 16 terms - sum of the first 15 terms
= 1464 - 1290
= 174
Now that we know the common difference, we can find t16 by adding the common difference to t15 (the 15th term).
t16 = t15 + d
To find S20 (the sum of the first 20 terms), we can use the formula for the sum of an arithmetic series:
S20 = (n/2)(2a + (n-1)d)
where:
n = number of terms
a = first term
d = common difference
Since we already know the sum of the first 15 terms, we can find the sum of the first 20 terms by subtracting the sum of the first 15 terms from the sum of the first 20 terms.
S20 = sum of the first 20 terms - sum of the first 15 terms
Therefore, we need to find the sum of the first 20 terms using the formula mentioned above, and then subtract the sum of the first 15 terms to get S20.