Home
Class 12
MATHS
Let a1,a2,a3…., a49 be in A.P . Such th...

Let `a_1,a_2,a_3…., a_49` be in A.P . Such that `underset(k=0)overset(12)Sigma a_(4k+1)=416` and `a_9+a_(43)=66` .If `a_1^2+a_2^2 +…+ a_(17)` = 140 m then m is equal to

A

66

B

68

C

34

D

33

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `a_(1), a_(2), a_(3),...a_(49)` are in AP
`underset(k=1)overset(12)sum a_(4k +1) = 416 and a_(9) + a_(43) = 66`
Let `a_(1) = a and d` = common difference
`:' a_(1) + a_(5) + a_(9) + ...+ a_(49) = 416`
`:. a + (a + 4d) + (a + 8d) + ...+ (a + 48d) = 416`
`rArr (13)/(2) (2a + 48d) = 416`
`rArr a + 24d = 32`...(i)
Also `a_(9) + a_(43) = 66`
`:. a + 8d + a + 42d = 66`
`rArr 2a + 50d + 66`
`rArr a + 25d = 33`...(ii)
solving Eqs. (i) and (ii), we get
`a = 8 and d =1`
Now, `a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + ...+ a_(17)^(2) = 140m`
`8x^(2) + 9^(2) + 10^(2) + ...+ 24^(2) = 140 m`
`rArr (1^(2) + 2^(2) + 3^(2) + ...+ 24^(2)) - (1^(2) + 2^(2) + 3^(2) + ...+ 7^(2)) = 140 m`
`rArr (24 xx 25 xx 49)/(6) - (7xx 8 xx 15)/(6) = 140 m`
`rArr (3xx 7 xx 8 xx 5)/(6) (7 xx 5 -1) = 140 m`
`rArr 7 xx4 xx 5 xx 34 = 140 m`
`rArr 140 xx 34 = 140 m rArr m = 34`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let a_1,a_2,a_3…., a_49 be in A.P . Such that Sigma_(k=0)^(12) a_(4k+1)=416 and a_9+a_(43)=66 .If a_1^2+a_2^2 +…+ a_(17) = 140 m then m is equal to

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then common ratio of G.P can be

Let a_(1),a_(2),a_(3),….,a_(4001) is an A.P. such that (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+...+(1)/(a_(4000)a_(4001))=10 a_(2)+a_(400)=50 . Then |a_(1)-a_(4001)| is equal to

Let a_(1), a_(2), a_(3), a_(4) be in A.P. If a_(1) + a_(4) = 10 and a_(2)a_(3) = 24 , them the least term of them is

If a_(1), a_(2), ……., a_(n) are in A.P. with common differece d != 0 , then (sin d) [sec a_(1) sec a_(2) + sec a_(2) sec a_(3) + .... + sec a_(n - 1) sec a_(n)] is equal to

If a_1,a_2,a_3…a_n are in H.P and f(k)=(Sigma_(r=1)^(n) a_r)-a_k then a_1/f(1),a_2/f(3),….,a_n/f(n) are in

Le a_1, a_2, a_3, ,a_(11) be real numbers satisfying a_2=15 , 27-2a_2>0a n da_k=2a_(k-1)-a_(k-2) for k=3,4, , 11. If (a1 2+a2 2+...+a 11 2)/(11)=90 , then the value of (a1+a2++a 11)/(11) is equals to _______.

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

Let a_1, a_2, ,a_(10) be in A.P. and h_1, h_2, h_(10) be in H.P. If a_1=h_1=2a n da_(10)=h_(10)=3,t h e na_4h_7 is

Let a_1, a_2, a_3, ?a_10 are in G.P. if a_3/a_1 =25 then a_9/a_5 is equal to (A) 5^4 (B) 4.5^4 (C) 4.5^3 (D) 5^3