Subjective Type

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

Solution

It is given that the $$k^{th}$$ term of the A.P. is $$5k +1$$.

Thus required sum is, $$=\sum_{k=1}^n(5k+1)=5\sum_1^n k+\sum_1^n1$$

$$\quad \displaystyle =5\frac{n(n+1)}{2}+n$$ [by using$$\sum_{i=1}^{n} k =1 + 2 + 3 +… + n = \dfrac{n(n+1)}{2}$$]

$$\quad =\dfrac{1}{2}n(5n+7)$$

SIMILAR QUESTIONS

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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:

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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.

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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

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

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

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

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

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