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.Mathematics

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