Question

What is the common difference of an A.P. in which a¹⁰ -a⁸=42?
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Answer 1

a^10 = a+(n-1)d

= a+(10-1)d

= a+9d ___(i)

a^8 = a+(n-1)d

= a+(8-1)d

= a+7d ___(ii)

a^10 - a^8 = 42

a+9d - a+7d = 42 ___[from(i),(ii)]

9d+7d = 42

16d = 42

d = 42/16

d = 21/8

Answer 2

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}\star$

d = 21/8

$\huge\star{\underline{\mathtt{\red{E}\pink{X}\green{P}\blue{L}\purple{A}\orange{N}\pink{A}\green{T}\blue{I}\purple{O}\orange{N}}}}\star$

= a+(n-1)d

= a+(10-1)d

= a+9d ___(i)

a^8 = a+(n-1)d

= a+(8-1)d

= a+7d ___(ii)

a^10 - a^8 = 42

a+9d - a+7d = 42 ___[from(i),(ii)]

9d+7d = 42

16d = 42

d = 42/16

$\huge\star{\underline{\mathtt{\red{R}\pink{E}\green{M}\blue{A}\purple{R}\orange{K}}}}\star$

Hope this answer will help you.✌️