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?
![question image](http://images.topperlearning.com/topper/new-ate/top_mob167447642752073419420230123_174737.jpg)
Asked by sakshinde95 | 23 Jan, 2023, 17:50: 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, 18:32: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by lp9128437598 | 10 Jun, 2024, 10:34: AM
CBSE 10 - Maths
Asked by deepikaselvam2009 | 20 Feb, 2024, 20:57: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 16 Jan, 2024, 20:46: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 15 Jan, 2024, 10:56: AM
CBSE 10 - Maths
Asked by skandachiranjeevin | 06 Dec, 2023, 19:08: PM
CBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 23:24: PM
CBSE 10 - Maths
Asked by latayadav23 | 17 Oct, 2023, 20:39: PM
CBSE 10 - Maths
Asked by ananya_monica | 28 Sep, 2023, 19:07: PM
CBSE 10 - Maths
Asked by simmysingh1aug | 20 Sep, 2023, 22:20: PM
CBSE 10 - Maths
Asked by bkhaiwangkonyak | 07 Mar, 2023, 16:35: PM