Question

If Sn = n - 5n, find S2, S5, S7 and S6 - S5.

a) S2 = -1
b) S5 = -5
c) S7 = -9
d) S6 - S5 = 4

Answer 1

The calculated terms using the formula Sn = n - 5n do not match the options provided in the question. This suggests there may be an error in the question or the answers given. The correct calculations for S2, S5, S7, and S6 - S5 are provided.

Step-by-step explanation:

Given the sequence formula Sn = n - 5n, we can find the specific terms of the sequence by substituting the given values of n.

• To find S2, substitute n = 2 into the formula: S2 = 2 - 5(2) = -8, which doesn't match the answer list provided.
• To find S5, substitute n = 5: S5 = 5 - 5(5) = -20, which isn't listed in the answer options.
• To find S7, substitute n = 7: S7 = 7 - 5(7) = -28, not matching the given options.
• For S6 - S5, first find S6 by substituting n = 6, which gives S6 = 6 - 5(6) = -24. Then use the previously found value for S5: S6 - S5 = -24 - (-20) = -4, which also doesn't align with the given answers.

However, based on the question provided there seem to be a mismatch with the calculated results and the listed answers, suggesting there may be a typo in the sequence formula or in the provided answers.