As worded the question makes very little sense. What does “S31” indicate? Is this the 31st value in a series, and you’re expected to find the first value in the series (“a1”)? What does “d” indicate with its -1.5 value?
Generally in order to find a regular series you need either of two things:
1. Three values, minimum, in order to view the pattern in order to make predictions about subsequent and antecedent values, or
2. One value and the “operation” to be performed to obtain the next (or previous) value.
(If the series is irregular, then more knowledge may be required. For example, if the series is: add 1 to the first value, add 2 to the second, add 3 to the third, and then repeat… then at least 4 terms are needed… or each of those operations, and at least two consecutive values in the series.)
So, for example, in the series 2, 4, 6 you know that the next value is “8”, because each of the numbers in the series is x+2, where “x” = a number in the series.
Or if you know that one of the numbers in the series is “16” and the operation is “add two to each value in the series to get the next value” (this is the same series, by the way), then you know that the next number in the series is 18 (= 16 + 2).
And since each value in that series can also be represented by its ordinal number * 2, then the 31st value in that series = 31 * 2 = 62.
But I don’t know what your terms mean in your question, so I can’t even hazard a guess at your series.
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