Let 3, 6, 9, 12,…. upto 78 terms and 5, 9, 13, 17,…. upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to…………
Let 3, 6, 9, 12,…. upto 78 terms and 5, 9, 13, 17,…. upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to…………
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1 Answer
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First common term to both AP’s is 9
t78 of
t59 of
nth common term
9 + (n – 1) 12
n <
Now sum of 19 terms with a = 9, d = 12
Similar Questions for you
First term = a
Common difference = d
Given: a + 5d = 2 . (1)
Product (P) = (a1a5a4) = a (a + 4d) (a + 3d)
Using (1)
P = (2 – 5d) (2 – d) (2 – 2d)
-> = (2 – 5d) (2 –d) (– 2) + (2 – 5d) (2 – 2d) (– 1) + (– 5) (2 – d) (2 – 2d)
= –2 [ (d – 2) (5d – 2) + (d – 1) (5d – 2) + (d – 1) (5d – 2) + 5 (d – 1) (d – 2)]
= –2 [15d2 – 34d + 16]
at
-> d = 1.6
a, ar, ar2, ….ar63
a+ar+ar2 +….+ar63 = 7 [a + ar2 + ar4 +.+ar62]
1 + r = 7
r = 6
S20 = [2a + 19d] = 790
2a + 19d = 79 . (1)
2a + 9d = 29 . (2)
from (1) and (2) a = –8, d = 5
= 405 – 10
= 395
3, 7, 11, 15, 19, 23, 27, . 403 = AP1
2, 5, 8, 11, 14, 17, 20, 23, . 401 = AP2
so common terms A.P.
11, 23, 35, ., 395
->395 = 11 + (n – 1) 12
->395 – 11 = 12 (n – 1)
32 = n – 1
n = 33
Sum =
=
= 6699
3, a, b, c are in A.P.
a – 3 = b – a (common diff.)
2a = b + 3
and 3, a – 1, b + 1 are in G.P.
a2 + 1 – 2a = 3b + 3
a2 – 8a + 7 = 0 &n
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