Two arithmetic sequence have same common difference.If their first term are 5,8 respectively,what is the difference between their eleventh terms if the product of the eleventh term is 2160.find the eleventh term of both sequences

Hello Salma dear, let d be the common difference
So eleventh term in first case 5 + 10 d and in second sequence 8 + 10 d
Difference between their 11th terms = 3
Product is (5 + 10d) ( 8 +10d) = 2160 [GIVEN]
OR 5 (1+2d) * 2 (4 + 5d) = 2160
==> (1+2d)(4 +5d) = 216
==> 4 + 13d + 10 d^2 = 216
===> 10 d^2 + 13 d - 212 = 0
Could be factored as ( d - 4) ( 10d + 53) = 0
So d = 4 is acceptable
Hence their eleventh terms are 45 and 48

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