Question

For the AP : 1/4 , -1/4 , -3/4, -5/4................,write the first term a and the common difference d . And find the 7th term?????????????????????????????????????

Answer 1

SOLUTION:-

Given

▪︎ Ap = 1/4, -1/4, -3/4,-5/4

To find

▪︎ First term

▪︎ Common difference

▪︎ 7th term

Explanation

▪︎ AP= 1/4,-1/4,-3/4,-5/4

First term = 1/4

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Common difference

= -1/4-1/4

= -1-1 /4

= -2/4

= -1/2

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7th Term

a= 1/4

d= -1/2

an= a+(n-1)×d

a7 = 1/4+(7-1)×-1/2

$= \frac{1}{4} + (7 - 1) \times ( \frac{ - 1}{2} )$

$= \frac{1}{4} + ( \frac{ - 7}{2} + \frac{1}{2} )$

$= \frac{1}{4} + ( \frac{ - 7 + 1}{2} )$

$= \frac{1}{4} + ( \frac{ - 6}{2} )$

$= \frac{1}{4} - \frac{6}{2}$

$= \frac{1 - 12}{4}$

$= \frac{ - 11}{4}$

______________________________

Hence

• First term = 1/4

• Common difference = -1/4

• 7th Term = -11/4

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Add for your Knowledge ⤵️⤵️

▪︎ an= a+(n-1)×d

▪︎nth term from the end = (l-(n-1)d

Where l= last term , d= Common difference

a= first term

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Answer 2

The terms which are given there that are

1/4, -1/4, -3/4

1/4= a1

-1/4=a2

-3/4=a3

So the first term is 1/4

To find common difference the formula is

d=a2-a1

so,-1/4-(-3/4)

-1/4+3/4

2/4

1/2 is the common difference

To find the seventh term

a7=?

The formula is an= a+(n+1)d

so here n is 7, a=1/4

d is nothing but common difference that is 1/2

applying to the formula

a7=1/4+(7-1) 1/2

a7= 1/4+6×1/2

a7=1/4+3 [In the above line we have

a7= 13/4 divided 6×1/2 that is 3.]