MyQuestionIcon

1

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

nth Term of A.P

Let a1, a2,...

Question

Let $a_{1}, a_{2}, a_{3}$ and $a_{4}$ be in AP. If $a_{1} + a_{4} = 10$ and $a_{2} \cdot a_{3} = 24$ , then the least term of them is

A

1

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

B

2

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

C

3

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

D

4

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

E

5

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

Open in App

Solution

The correct option is B $2$
Let the four terms in an AP are $(a - 3 d), (a - d), (a + d)$ and $(a + 3 d)$ .
Given, $a_{1} + a_{4} = 10$
$\Rightarrow (a - 3 d) + (a + 3 d) = 10$
$\Rightarrow 2 a = 10 \Rightarrow a = 5$
and $a_{2} \cdot a_{3} = 24$
$\Rightarrow (a - d) (a + d) = 24$
$\Rightarrow (a^{2} - d^{2}) = 24$
$\Rightarrow 25 - d^{2} = 24$
$\Rightarrow d^{2} = 1$
Therefore, $d = \pm 1$
When $(d = 1)$ , then terms are : $2, 4, 6, 8$
and when $(d = - 1)$ , then terms are: $8, 6, 4, 2$ .

Suggest Corrections

thumbs-up

0

Similar questions

a_{1}, a_{2}, a_{3}, a_{4}

are terms of an AP, then the relation between them is

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}, a_{2}, a_{3}, a_{4}

are in AP, then

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{1}{\sqrt{a_{3}} + \sqrt{a_{4}}}

a_{1}, a_{2}, a_{3}, a_{4}, . . {. ., a}_{20}

a_{1} + a_{20} = 45

a_{1} + a_{2} + a_{3} + a_{4}, . . {. . + a}_{20}

If $a_{1}, a_{2}, a_{3}, a_{4}$ be the coefficeints of four consecutive terms in the expansion of $(1 + x)^{n}$ then prove that
$\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{(a_{3} + a_{4})} = \frac{2 a_{2}}{(a_{2} + a_{3})} .$

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Arithmetic Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

nth Term of A.P

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon