Question

The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 6. The common difference of the AP is.......

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Correct Question :-

The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is

$\bf{\underline{\underline\red{Given:-}}}$

• The 5th term of an AP is 20.

• The sum of 7th and 11th terms is 6.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The common difference of the AP.

$\bf{\underline{\underline\green{Solution:-}}}$

As we know that:-

The nth term of the AP is given by the formula:-

$\boxed{ \rm \leadsto a_{n} = a + (n - 1)d }$

Here:-

• a = first term

• n = number of terms.

• d = common difference

The 5th term = 20

${ \rm \implies a_{5} = 20 }$

${ \rm \implies a + (5 - 1)d= 20 }$

${ \rm \implies a + 4d= 20......(i) }$

Sum of 7th term and 11th term is 64

${ \rm \implies a_{7} + a_{11}= 64}$

${ \rm \implies a + (7 - 1)d + a + (11 - 1)d= 64}$

${ \rm \implies a + 6d + a + 10d= 64}$

${ \rm \implies a + a + 6d + 10d= 64}$

${ \rm \implies 2a+ 16d= 64}$

Dividing the whole equation by 2

${ \rm \implies a+ 8d= 32.....(ii)}$

Subtracting equation (i) from (ii)

${ \rm \implies a+ 8d - (a + 4d) = 32 - 20}$

${ \rm \implies a+ 8d - a - 4d = 12}$

${ \rm \implies 4d= 12}$

${ \rm \implies d= \dfrac{12}{4} }$

${ \rm \implies d= 3}$

$\underline{\boxed{ \purple{\rm \therefore Common \: difference \: of \: the \: AP= 3}}}$