Product of the fourth term and the fifth term of an arithmetic progres

1.	Product of the fourth term and the fifth term of an arithmetic progression is 456. Division of the ninth term by the fourth term of the progression gives quotient as 11 and the remainder as 10. Find the first term of the progression. (a) – 52 (b) – 42 (c) – 56 (d) – 66
Answer» Correct option (d) – 66 Explanation: A factor search for factor pairs of 456 give us the following possibilities. 1,456; 2,228; 3,152; 4,114; 6,76; 8,57; 12,38 & 19,24. A check of the conditions given in the problem, tells us that if we take 12 as the 4^th term and 38 as the 5^thterm, we would get the series till 9 terms as: −66,−40,−14,12,38,64, 90,116,142. In this series we can see that the division of the 9^th term by the 4^th term gives us a quotient of 11 and a remainder of 10. Hence, the required first term is −66.

Product of the fourth term and the fifth term of an arithmetic progression is 456. Division of the ninth term by the fourth term of the progression gives quotient as 11 and the remainder as 10. Find the first term of the progression. (a) – 52 (b) – 42 (c) – 56 (d) – 66

Answer»

Correct option (d) – 66

Explanation:

A factor search for factor pairs of 456 give us the following possibilities. 1,456; 2,228; 3,152; 4,114; 6,76; 8,57; 12,38 & 19,24. A check of the conditions given in the problem, tells us that if we take 12 as the 4^th term and 38 as the 5^thterm, we would get the series till 9 terms as: −66,−40,−14,12,38,64, 90,116,142. In this series we can see that the division of the 9^th term by the 4^th term gives us a quotient of 11 and a remainder of 10. Hence, the required first term is −66.

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