The corresponding terms of two A.P.s are multiplied together to give series 240, 336, 440, …. Find the 10th term of series: please answer quickly
Answers
Given : The corresponding terms of two A.P.s are multiplied together to give series 240, 336, 440, ….
To find : 10th term of series
Solution:
Let say Two AP Series are
a , a + d , a + 2d . .............
&
A , A + D , A + 2D ,..................
aA = 240
(a + d)(A + D) = 336
=> aA + aD + Ad + dD = 336
=> 240 + aD + Ad + dD = 336
=> aD + Ad + dD = 96
(a + 2d)(A + 2D) = 440
=> aA + 2aD + 2Ad + 4dD = 440
=> 240 + 2aD + 2Ad + 4dD = 440
=> 2aD + 2Ad + 4dD = 200
=> aD + Ad + 2dD = 100
=> dD = 4
=> aD + Ad = 92
10th term of series = (a + 9d)(A + 9D)
= aA + 9aD + 9Ad + 81dD
= 240 + 9(92) + 81*4
= 240 + 828 + 324
= 1392
10th term of series = 1392
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