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Question

If A times the 7th term of an AP is equal to 12 times the 12th term then find the 19th term.


Solution

$$AT_r=12\cdot T_{12}$$          $$T_{19}=a+17d$$ ……….$$(1)$$
$$A(a+6d)=12(a+11d)$$
$$A(a+6d)=12a+32d$$
$$Aa+6Ad=12a+132d$$
$$(12a-Aa)+132d-6Ad=0$$
$$a(12-A)+d(132-6A)=0$$ ……..$$(2)$$
On comparing $$(1)$$ and $$(2)$$:-
$$132-6A=17$$
$$6A=132-17$$
$$6A=115$$
$$A=\dfrac{115}{6}$$
$$A=\dfrac{35}{2}$$
$$12-A=1$$
$$A=11$$
Incomplete question.

1177477_1242465_ans_05d6fc1a04c54e2a9fe7afa6aa8ade89.jpg

Mathematics

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