Chapter 14: Q52. (page 768)

Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .

Short Answer

Expert verified

The first five terms of the sequence are $3, 11, 27, 59 and 123$ .

Step by step solution

Step 1. Write down the given information.

The given sequence has $a_{1} = 3 and a_{n + 1} = 2 a_{n} + 5$ .

Step 2. Evaluating first five terms of the given sequence.

Since, the first term is $a_{1} = 3$ of the given sequence. Therefore, the remaining four terms can be obtained by plugging $n = 1, 2, 3, 4$ to get $a_{2}, a_{3}, a_{4} and a_{5}$ in the given sequence $a_{n + 1} = 2 a_{n} + 5$ .

For $n = 1$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(1) + 1} = 2 a_{(1)} + 5.... (For n = 1) \\ a_{2} = 2 (3) + 5.... (∵ a_{1} = 3) \\ a_{2} = 11 \end{matrix}$

For $n = 2$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(2) + 1} = 2 a_{(2)} + 5.... (For n = 2) \\ a_{3} = 2 (11) + 5.... (∵ a_{2} = 11) \\ a_{3} = 27 \end{matrix}$

For $n = 3$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(3) + 1} = 2 a_{(3)} + 5.... (For n = 3) \\ a_{4} = 2 (27) + 5.... (∵ a_{3} = 27) \\ a_{4} = 59 \end{matrix}$

For $n = 4$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(4) + 1} = 2 a_{(4)} + 5.... (For n = 4) \\ a_{5} = 2 (59) + 5.... (∵ a_{4} = 59) \\ a_{5} = 123 \end{matrix}$

Since, $a_{1} = 3, a_{2} = 11, a_{3} = 27, a_{4} = 59 and a_{5} = 123$ . Therefore, the first five terms of the sequence are $3, 11, 27, 59 and 123$ .

Step 3. Conclusion.

The first five terms of the sequence are $3, 11, 27, 59 and 123$ .

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Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Evaluating first five terms of the given sequence.

Step 3. Conclusion.

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Find first five terms of the sequence in which a1=3,an+1=2an+5.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Evaluating first five terms of the given sequence.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Logic and Functions

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Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .