Sequences And Series Question 22
Question 22 - 01 February - Shift 2
The sum of the common terms of the following three arithmetic progressions.
$3,7,11,15$, 399
$2,5,8,11$ 359 and
$2,7,12,17$ 197 , is equal to
Show Answer
Answer: 321
Solution:
Formula: General Term of an AP
$ \begin{aligned} & 3,7,11,15, \ldots \ldots \ldots \ldots, 399 , ; ;d_1=4 \\ & 2,5,8,11, \ldots \ldots \ldots \ldots . ., 359, ; ; d_2=3 \\ & 2,7,12,17, \ldots \ldots, 197 , ; ; d_3=5 \\ & \operatorname{LCM}\left(d_1, d_2, d_3\right)=60 \\ & \end{aligned} $
Common terms are 47, 107, 167
Sum =321
