The fourth term of an A.P. is ten times the first. Prove that the sixth term is four times as great as the second term.

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Solution

Let first term of AP be $a$ , and common difference be $d$ .

According to question,

$10 a = a + 3 d$

$⟹ d = 3 a$

Second term, $= a + d = 4 a$ ........(1)

sixth term , $= a + 5 d = 16 a$ .........(2)

From (1) and (2),

sixth term is four times as great as second term.

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The fourth term of an A.P. is ten times the first. Prove that the sixth term is four times as great as the second term.

Let first term of AP be a, and common difference be d.According to question,10a=a+3d⟹d=3aSecond term, =a+d=4a ........(1)sixth term , =a+5d=16a .........(2)From (1) and (2),sixth term is four times as great as second term.

Let first term of AP be $a$ , and common difference be $d$ .

According to question,

$10 a = a + 3 d$

$⟹ d = 3 a$

Second term, $= a + d = 4 a$ ........(1)

sixth term , $= a + 5 d = 16 a$ .........(2)

From (1) and (2),

sixth term is four times as great as second term.