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CBSE Class 10 Answered

the sum of fourth and eight terms of an A.P is 54 and their product is 665. find the sum of the first thirty terms of an A.P​
Asked by sakshinde95 | 23 Jan, 2023, 05:50: PM
Expert Answer
Let a be the first term and d be the common difference of A.P
 
Fourth term of A.P = a + 3d
 
Eighth term of A.P. = a + 7d
 
Sum of fourth term and eighth term = 2 a + 10 d = 54
 
Hence , we get , a + 5 d = 27 ........................(1)
 
Product of fourth term and eight term is 665.
 
Hence we have ,  ( a + 3d ) ( a + 7d ) = 665
 
Let us eliminate first term of A.P , i.e. a in above expression  ( 2) using eqn.(1)
 
[ ( 27- 5d )  + 3d ]  [ (27-5d) + 7d ) = 665
 
( 27 - 2d) ( 27 + 2d ) = 665
 
729 - 4 d2 = 665 
 
hence we get d = 4
 
by substituting d in eqn.(1) , we get a = 7
 
sum S of 30 terms is determined from following formula
 
S = (n/2) [ 2 a + (n-1) d ]
 
where n is number of terms.
 
Sum of 30 terms = (30/2) [ 14 + 29 × 4 ] = 1950
 





Answered by Thiyagarajan K | 23 Jan, 2023, 06:32: PM

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