Question

6. Find the 6" term of the A.P. 17, 11, 14,
दी गई समान्तर श्रेणी का छटा पद ज्ञात कीजिए। 17, 11, 14,
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-
TE.1
14​

Answer 1

SOLUTION

TO DETERMINE

The 6 th term of the A.P. 17, 11, 14,.....

FORMULA TO BE IMPLEMENTED

If in an arithmetic progression (AP)

First term = a

Common Difference = d

Then n th term of the AP

$= \sf{a + (n - 1)d}$

EVALUATION

Here the given Arithmetic progression (AP) is

17, 11, 14,.....

First term = a = 17

Second Term - First Term = - 6

Third term - Second Term = 3

So the difference is not same

So the given terms are not in AP

CORRECTION IN THE QUESTION

If the question is as below :

Find the 6 th term of the A.P. 17, 11, 14,.....

EVALUATION

Here the given Arithmetic progression (AP) is

17, 14, 11,.....

First term = a = 17

Second Term - First Term = - 3

Third term - Second Term = - 3

Common Difference = d = - 3

Here n = 6

6th term of the AP

$= \sf{a + (n - 1)d}$

$= \sf{17 + 5d}$

$= \sf{17 + (5 \times - 3)}$

$= 17 - 15$

$= 2$

Hence the 6 th term of the A.P. 17, 14, 11,..... is 2

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Answer 2

ARITHMETIC PROGRESSION

Given :-

A.P. : 17, 11, 14,...

To Find :-

6th term of the A.P.

Solution :-

In order to calculate the 6th term of the given A.P. we should know some basic terms used in arithmetic progression.

a1 = First term of the A.P.

d = Common difference in the A.P.

n = No. of terms in an A.P.

an = Last term in the A.P = a + (n-1)d

ATQ,

a1 = 17

d = a2 - a1 = 11 - 17 = - 6

or

a3 - a2 = 14 - 11 = 3

The value of d should be same for any value in the A.P.. If the common difference isn't same then the given series is not an A.P.

∵ The value in the given series isn't same if calculated with different terms.

∴ It is not an A.P.

Correct form of the A.P. can be :-

17, 14, 11,...

Here,

a1 = 17

a2 = 14

a3 = 11

d = 14 - 17 = - 3

or

d = 11 - 14 = - 3

∴ Common difference d is same here,

∴ We can go further and calculate the 6th term of the A.P.

a6 = a + 5d

    = 17 + 5(- 3)

    = 17 - 15

    = 2

⇒ The 6th term of the A.P. is 2.

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