Question

If in an AP, 8th term is 4 and 16th term is -20, then find the common difference of the given AP.​

Answer 1

Given :

If in an AP, 8th term is 4 and 16th term is -20 .

To Find :

Common Difference of the A.P .

Solution :

As Given that ,

$\longmapsto\tt{a+7d=4}$

$\longmapsto\tt{a+15d=-20}$

Now By Elimination Method :

$\longmapsto\tt{{\not{a}}+7d=4}$

$\longmapsto\tt{{\not{a}}+15d=-20}$

$\longmapsto\tt{-8d=24}$

$\longmapsto\tt{d=\cancel\dfrac{24}{-8}}$

$\longmapsto\tt\bf{d=-3}$

So , The Common Difference of the given A.P is -3 .

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${a}_{n}=a + (n-1) × d$

General Form = a , a + d , a + 2d ...

s = n/2 [2a (n-1) × d]

Here :

n = nth term

a = first term of the a.p

s = sum of nth terms

d = common difference

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