Request a call back

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

## Concept Videos

CBSE 10 - Maths
Asked by bkhaiwangkonyak | 07 Mar, 2023, 04:35: PM ANSWERED BY EXPERT
CBSE 10 - Maths
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 ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by d7016880266 | 20 Jan, 2023, 08:14: PM ANSWERED BY EXPERT
CBSE 10 - Maths ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by Keerthanaambika48 | 13 Jul, 2021, 09:44: AM ANSWERED BY EXPERT
CBSE 10 - Maths ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by maulaali35 | 24 Oct, 2020, 08:00: AM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by Anubhavjain599 | 25 Aug, 2020, 10:16: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by seeni2005 | 17 Aug, 2020, 12:42: AM ANSWERED BY EXPERT
CBSE 10 - Maths
Plz solve this question Asked by Deepakaryan571 | 09 Aug, 2020, 12:18: PM ANSWERED BY EXPERT