Subjective Type

$$\displaystyle{ a }_{ 1 }=3,{ a }_{ n }={ 3a }_{ n-1 }+2$$ for all $$ n>1$$

Solution

We have, $$\displaystyle{ a }_{ 1 }=3,{ a }_{ n }={ 3a }_{ n-1 }+2 \forall n>1$$
$$\Rightarrow

{ a }_{ 2 }={ 3 }{ a_1 }+2=3(3)+2=11\\ { a }_{ 3 }={ 3 }{ a_2

}+2=3(11)+2=35\\ { a }_{ 4 }={ 3 }{ a_3 }+2=3(35)+2=107\\ { a }_{ 5 }={ 3

}{ a_4 }+2=3(107)+2=323$$
Hence, the first five terms of the sequence are $$3, 11, 35, 107$$ and $$323$$.
Corresponding series is $$3 + 11 + 35 + 107 + 323 + ...$$

SIMILAR QUESTIONS

Sequences and Series

If $$a_1, a_2, a_3,....a_n$$ are in A.P. and $$a_1+ a_4 + a_7 + ..... + a_{16} = 114$$, then $$a_1 + a_6 + a_{11} + a_{16}$$ is equal to:

Sequences and Series

If the sum of the first n terms of the series $$\sqrt{3}+\sqrt{75}+\sqrt{243}+\sqrt{507}+....$$ is $$435\sqrt{3}$$, then n equals.

Sequences and Series

Let $$a_{1},\ a_{2},\ a_{3},\ \ldots,\ a_{100}$$ be an arithmetic progression with $$a_{1}=3$$ and $$S_{p}$$ is sum of 100 terms . For any integer $$n$$ with $$1\leq n \leq 20$$, let $$ m=5n$$. If $$\dfrac{S_{m}}{S_{n}}$$ does not depend on $$n$$, then $$a_{2}$$ is

Sequences and Series

Find the sum of odd integers from $$1$$ to $$2001$$.

Sequences and Series

Find the sum to $$n$$ terms of the $$A.P.$$, whose $$k^{th}$$ term is $$5k+1$$.

Sequences and Series

If the sum of first $$p$$ terms of an A.P.is equal to the sum of the first $$q$$ terms, then find the sum of the first $$(p+q)$$ terms.

Sequences and Series

Sum of the first $$p, q$$ and $$r$$ terms of an A.P. are $$a,b$$ and $$c$$ respectively. Prove that $$\displaystyle \frac { a }{ p } (q-r)+\frac { b }{ q } (r-p)+\frac { c }{ r } (p-q)=0$$

Sequences and Series

Between $$1$$ and $$31$$, $$m$$ numbers have been inserted in such a way that the resulting sequence is an $$A.P$$. and the ratio of $$\displaystyle { 7 }^{ th }$$ and $$(n-1)^{th}$$ numbers is $$5 : 9$$ . Find the value of $$n$$.

Sequences and Series

$$\displaystyle 1\times 2+2\times 3+3\times 4+4\times 5+...$$

Sequences and Series

$$\displaystyle 1\times 2\times 3 +2\times 3\times 4+3 \times 4\times 5+...$$

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