Question

what is the common difference of an A.P in which a10-a8=42
a)15
b)12
c)9
d)21​

Answer 1

Answer:

Your question's answer

Step-by-step explanation:

a10=a+(10-1)×d

a8= a+(8-1)×d

using a10-a8 =42

a+9d-(a+7d)=42

a+9d-a-7d=42

2d=42

d=42/2

d=21

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The common difference of an A.P in which

$\sf{a_{10} - a_8\: } = 42 \: \: \: \: is$

a) 15

b) 12

c) 9

d) 21

FORMULA TO BE IMPLEMENTED

If in an arithmetic progression

First term = a and common difference = d

Then nth term of the Arithmetic progression is

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

EVALUATION

Let a be the First term and d be the Common Difference of the given Arithmetic progression

Then

$\sf{a_{10} = a + (10 - 1)d \: }$

$\implies \sf{a_{10} = a + 9d \: }$

Again

$\implies \sf{a_{8} = a + (8 - 1)d \: }$

$\implies \sf{a_{8} = a + 7d \: }$

Now by the given condition

$\sf{a_{10} - a_{8} = 42\: }$

$\implies \sf{(a + 9d) - (a + 7d) = 42\: }$

$\implies \sf{a + 9d- a - 7d= 42\: }$

$\implies \sf{2d= 42\: }$

$\implies \sf{d = 21\: }$

FINAL ANSWER

The common difference of an A.P in which

$\sf{a_{10} - a_8\: } = 42 \: \: \: \: is$

d) 21

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