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
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
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by simmysingh1aug | 20 Sep, 2023, 10:20: PM
CBSE 10 - Maths
Asked by bkhaiwangkonyak | 07 Mar, 2023, 04:35: PM
CBSE 10 - Maths
Asked by sakshinde95 | 23 Jan, 2023, 05:50: PM
CBSE 10 - Maths
Asked by d7016880266 | 20 Jan, 2023, 08:14: PM
CBSE 10 - Maths
Asked by jaiprakashprasadr | 17 Jul, 2022, 11:03: PM
CBSE 10 - Maths
Asked by Keerthanaambika48 | 13 Jul, 2021, 09:44: AM
CBSE 10 - Maths
The sum of the first 7 terms of an A.P is 182 if its 4th ans 17th terms are in ratio 1:5 find the Ap
Asked by madhutowari | 28 Jun, 2021, 07:56: PM
CBSE 10 - Maths
Asked by maulaali35 | 24 Oct, 2020, 08:00: AM
CBSE 10 - Maths
Asked by Anubhavjain599 | 25 Aug, 2020, 10:16: PM
CBSE 10 - Maths
Asked by seeni2005 | 17 Aug, 2020, 12:42: AM