MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Quantitative Aptitude

Progressions

Let a 1, a 2…...

Question

Let $a_{1}, a_{2} \dots a_{3 n}$ be an arithmetic progression with $a_{1} = 3$ and $a_{2} = 7$ . If $a_{1} + a_{2} + \dots + a_{3 n} = 1830$ , then what is the smallest positive integer m such that $m (a_{1} + a_{2} + \dots + a_{n}) > 1830$ ?

A

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

11

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
9

$a_{1} = 3 a_{2} = 7$
common difference = $d = 7 - 3 = 4 a_{3 n} = a_{1} + (3 n - 1) \times 4 = 3 + 12 n - 4 = 12 n - 1 3 + 7 + 11 + \dots + (12 n - 1) = 1830 3 n \frac{[6 + (3 n - 1) \times 4]}{2} = 1830 3 n [2 + 12 n] = 3660 n [1 + 6 n] = 610 6 n^{2} + n - 610 = 0 n = 10$
Therefore, $a_{10} = 3 + 9 \times 4 = 39 a_{1} + a_{2} + \dots + a_{10} = 3 + 7 + \dots + 39 = 5 \times 42 = 210 m \times 210 > 1830 m > 8$
Hence smallest integral value of m = 9.

Suggest Corrections

thumbs-up

0

Similar questions

a_{1}, a_{2}, . . . a_{3 n}

be an arithmetic progression with

a_{1} = 3

a_{2} = 7

a_{1} + a_{2} + . . . + a_{3 n} = 1830

then what is the smallest positive integer

m

m (a_{1} + a_{2} + . . . + a_{n}) > 1830 ?

a_{1}, a_{2}, a_{3}, \dots, a_{100}

be an arithmetic progression with

a_{1} = 3

S_{p}

is sum of 100 terms . For any integer

n

1 \leq n \leq 20

m = 5 n

\frac{S_{m}}{S_{n}}

does not depend on

n

a_{2}

If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ are in arithmetic progression, where $a_{1} > 0$ for all i.
Prove that $\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \dots + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{n - 1}{\sqrt{a_{1}} + \sqrt{a_{n}}}$

a_{1}, a_{2}, a_{3}, \dots \dots, a_{100}

be an arithmetic progression with

a_{1} = 3

S_{p} = \sum_{i = 1}^{p} a_{i}, 1 \leq p \leq 100

. For any integer n with

1 \leq n \leq 20

, let m = 5n. If

\frac{S_{m}}{S_{n}}

does not depend on n, then

a_{2}

The n^th term (general term) of an arithmetic progression, a₁, a₂, a₃, …, a_n, … where a₂ –a₁ = a₃ – a₂ = …. = d is:

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Fear of the Dark

QUANTITATIVE APTITUDE

Watch in App

explore_more_icon

Explore more

Other Quantitative Aptitude

Join BYJU'S Learning Program

CrossIcon