If the sum and product of the first three terms in an A.P. are 33 and 1155 , respectively, then a value of its 11^th term is

a - d, a, a + d Sum = 3a = 33 => a = 11 Terms: 11 - d, 11, 11 + d Product = 11(121 - d^2) = 1155 121 - d^2 = 105nd^2 = 16nd = ± 4 Terms are 7, 11, 15 or 15, 11, 17nt_11 = 7 + 10(4) = 47nt_11 = 15 + 10(-4) = -25

If the sum and product of the first three terms in an A... | Sequence & Series (Mathematics)

a - d, a, a + d $\\$ Sum = 3a = 33 $\Rightarrow$ a = 11 $\\$ Terms: 11 - d, 11, 11 + d $\\$ Product = 11(121 - d^2) = 1155 $\\$ 121 - $d^2$ = $105nd^2$ = 16nd = $\pm$ 4 $\\$ Terms are 7, 11, 15 or 15, 11, $\\$ $17nt_{11}$ = 7 + 10(4) = $47nt_{11}\\$ = 15 + 10(-4) = -25

Explanation

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