Question Type 6: Finding sum of first n terms given the values of other sums Bootcamps

Given that $S_{10}=150$ and $S_{6}=66$ for an arithmetic sequence, find $S_{4}$.

For an arithmetic sequence, the sum of the first 7 terms is 56 and the sum of the first 3 terms is 18. Find the sum of the first 5 terms.

Given the sum of the first 4 terms is 14 and the sum of the first 7 terms is 35 for an arithmetic sequence, find the sum of the first 10 terms.

The sum of the first 5 terms of an arithmetic sequence is 35 and the sum of the first 9 terms is 99. Find the sum of the first 7 terms.

Given the sum of the first 5 terms of an arithmetic sequence is 20 and the sum of the first 8 terms is 44, find the sum of the first 6 terms.

Given that $S_8=96$ and $S_3=21$ for an arithmetic sequence, find $S_6$.

Given the sum of the first 4 terms of an arithmetic sequence is 20 and the sum of the first 6 terms is 42, find the sum of the first 8 terms.

Given the sum of the first 8 terms is 40 and the sum of the first 14 terms is 91 for an arithmetic sequence, find the sum of the first 20 terms.

The sum of the first 9 terms of an arithmetic sequence is 81 and the sum of the first 12 terms is 132. Find the sum of the first 15 terms.