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Maharashtra Class 10 Answered

Find four consecutive terms in an A.p such that the sum of second and third terms is 18 and the product of the first and fourth term is 45
Asked by kshitijtambde | 10 Mar, 2019, 06:44: PM
answered-by-expert Expert Answer
let 4 terms of A.P. are  (a-d), a, (a+d), (a+2d)
 
sum of second and third terms = 2a+d = 18    or  a = 9-(d/2) ........(1)
 
product of first and fourth terms are  (a-d)(a+2d) = 45  .............(2)
 
let us substitute value of a from eqn.(1)  in eqn (2)  ,  [ 9 -(3/2)d ] [ 9 + (3/2)d ] = 81 - (9/4)d2 = 45   or  d2 = 16   or   d = 4
 
Let us substitute d value in eqn.(1) to get value of a.   we get a = 7
 
4 terms of A.P. are  3, 7, 11, 15
Answered by Thiyagarajan K | 10 Mar, 2019, 08:14: PM

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