Question 17 and 18, Exercise 4.1

Solutions of Question 17 and 18 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the indicated term of the sequence.$a_{n}=\log 10^{n} ; a_{43}$

Solution. Given: $$a_n = \log 10^n.$$ Then $$\begin{align*} a_{43} &= \log 10^{43} \\ &= 43 \cdot \log 10 \\ &= 43 \cdot 1 \\ &= 43 \end{align*}$$ Hence $a_{43}= 43$.

Find the indicated term of the sequence.$a_{n}=\ln e^{n} ; a_{67}$

Solution. Given: $$a_n = \ln e^n.$$ Then $$\begin{align*} a_{67} &= \ln e^{67} \\ &= 67 \cdot \ln e \\ &= 67 \cdot 1 \\ &= 67 \end{align*}$$

Hence $a_{67}= 67$.

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