Let N be the 8th term of the sequence 1440, 1716, 1848, whose terms are formed by multiplying the corresponding terms of an arithmetic progression Find 12 N
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Let a be the first term and d be their common difference of the AP.
Then, nth term of the AP T
n
=a+(n−1)d
Given, 8×T
8
=12×T
12
⇒8(a+(8−1)d)=12(a+(12−1)d)
⇒8(a+7d)=12(a+11d)
⇒2(a+7d)=3(a+11d)
⇒2a+14d=3a+33d
⇒a=−19d
So, T
20
=a+(20−1)d=−19d+19d=0
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