Obtain the sum of the first 56 terms of an A.P. Whose 18th and 39th te – InterviewSolution

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1.	Obtain the sum of the first 56 terms of an A.P. Whose 18th and 39th terms are 52 and 148 respectively. (1) Usint `t_(18)` and `t_(39)` find two simultaneous equations in variables a and d. (2) Using these equations, find `S_(56)`
Answer» Correct Answer - The sum of the first 56 terms is 5600 Let the first term of A.P. be a and the common difference d. `t_(n) = a+ ( n -1) d ` …(Formula) `:. T_(18) = a + ( 18-1) d ` `:. 52 = a+ 17d` ....(1) and `t_(39) a + ( 39-1)d` `:. 148 = a + 38d` ...(2) Adding equations (1) and (2) `52= a + 17d ` ...(1) `148 = a + 38 d ` ...(2) `bar( 200 = 2a + 55d)` ....(3) We have to find `S_(56 )` `S_(n) = ( n )/( 2) [2a + (n -1) d]` `:. S_(56) = ( 56)/( 2) [2a + ( 56-1) d ]` `= 28 (2a+ 55d]` `= 28( 200) ` ...[From (30] ` = 5600`

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