If for an A-P- a 5-a10-5 a-then a15 is-

Let a be first term and d be common difference A5 = a10 = 5×a so, a+4d = a+9d= 5a ——— (1) a+4d = a+9d(first case) = gt;0=5d = gt;d=0— (2) And also 5a=a ...

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Standard X

Mathematics

Arithmetic Progression

If for an A.P...

Question

If for an A.P. $a_{5} = a_{10} = 5 \times a$ , then $a_{15}$ is....

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Solution

Let $a$ be first term and $d$ be the common difference then given
$a_{5} = a_{10} = 5 \times a$
so, $a + 4 d = a + 9 d = 5 a$ ----------(1)
$a + 4 d = a + 9 d$ (first case)
$\Rightarrow a - a = 9 d - 4 d$
$\Rightarrow 0 = 5 d$
$\Rightarrow d = 0$ ----(2)
And also
$5 a = a + 4 d$ (2nd case)
$\Rightarrow 5 a - a = 4 d$
$\Rightarrow 4 a = 4 d$
$a = d = 0$ {from (2)}
Thus, $a_{15} = a + 14 d$
$= 0 + (14 \times 0)$
$∴ a_{15} = 0$

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If for an A.P. a5=a10=5×a, then a15 is....

Let a be first term and d be the common difference then givena5=a10=5×a so, a+4d=a+9d=5a ----------(1)a+4d=a+9d (first case)⇒a−a=9d−4d⇒0=5d⇒d=0----(2)And also5a=a+4d (2nd case)⇒5a−a=4d⇒4a=4da=d=0 {from (2)}Thus, a15=a+14d=0+(14×0)∴a15=0

If for an A.P. $a_{5} = a_{10} = 5 \times a$ , then $a_{15}$ is....