If the sum and product of the first three terms in an A.P. are 33 and

1.	If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is : (1) –25 (2) –35 (3) –36 (4) 25
Answer» Correct option (1) –25 Explanation: Let the three numbers in A.P. are a – d, a, a + d given that : a – d + a + d = 33 ⇒ a = 11 and (a – d)(a)(a + d) = 1155 ⇒ a(a² – d² ) = 1155 ⇒ 11(121 – d² ) = 1155 ⇒ d² = 16 ⇒ d = ±4 If d = 4 then first term a – d = 7 If d = –4 then first term a – d = 15 T₁₁ = 7 + 10(4) = 47 or T₁₁ = 15 + 10(–4) = –25

If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is : (1) –25 (2) –35 (3) –36 (4) 25

Answer»

Correct option (1) –25

Explanation:

Let the three numbers in A.P. are

a – d, a, a + d

given that : a – d + a + d = 33

⇒ a = 11

and (a – d)(a)(a + d) = 1155

⇒ a(a² – d² ) = 1155

⇒ 11(121 – d² ) = 1155

⇒ d² = 16

⇒ d = ±4

If d = 4 then first term a – d = 7

If d = –4 then first term a – d = 15

T₁₁ = 7 + 10(4) = 47

or T₁₁ = 15 + 10(–4) = –25

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If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is : (1) –25 (2) –35 (3) –36 (4) 25

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