If in any decreasing arithmetic progression, sum of all its terms, exc

1.	If in any decreasing arithmetic progression, sum of all its terms, except for the first term, is equal to –36, the sum of all its terms, except for the last term, is zero, and the difference of the tenth and the sixth term is equal to –16, then what will be first term of this series? (a) 16 (b) 20 (b) –16 (d) –20
Answer» Correct option (a) 16 Explanation: Since the difference between the tenth and the sixth terms is −16, the common difference would be −4. Using a trial and error approach with the options, we can see that if we take the first term as 16, we will get the series 16,12,8,4,0,−4,−8,−12,−16,−20. We can see that both the conditions given in the question are met by this series. Hence, the first term would be 16.

If in any decreasing arithmetic progression, sum of all its terms, except for the first term, is equal to –36, the sum of all its terms, except for the last term, is zero, and the difference of the tenth and the sixth term is equal to –16, then what will be first term of this series? (a) 16 (b) 20 (b) –16 (d) –20

Answer»

Correct option (a) 16

Explanation:

Since the difference between the tenth and the sixth terms is −16, the common difference would be −4. Using a trial and error approach with the options, we can see that if we take the first term as 16, we will get the series 16,12,8,4,0,−4,−8,−12,−16,−20. We can see that both the conditions given in the question are met by this series. Hence, the first term would be 16.

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