If the {n^{th}} terms of two arithmetic progr | vedclass

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(A) Let the ${n^{th}}$ terms of the two arithmetic progressions be $a_n = 3n + 8$ and $b_n = 7n + 15$.To find the ${12^{th}}$ term of the first $A.P.$

Vedclass · Accepted Answer

$4/9$

Vedclass · Answer

(A) Let the ${n^{th}}$ terms of the two arithmetic progressions be $a_n = 3n + 8$ and $b_n = 7n + 15$.To find the ${12^{th}}$ term of the first $A.P.$,substitute $n = 12$ into $a_n$:$a_{12} = 3(12) + 8 = 36 + 8 = 44$.To find the ${12^{th}}$ term of the second $A.P.$,substitute $n = 12$ into $b_n$:$b_{12} = 7(12) + 15 = 84 + 15 = 99$.The ratio of their ${12^{th}}$ terms is $\frac{a_{12}}{b_{12}} = \frac{44}{99}$.Simplifying the fraction by dividing both numerator and denominator by $11$,we get $\frac{44 \div 11}{99 \div 11} = \frac{4}{9}$.

If the ${n^{th}}$ terms of two arithmetic progressions $(A.P.)$ are $3n + 8$ and $7n + 15$,then the ratio of their ${12^{th}}$ terms will be:

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