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Sum of n Terms

If a1,a2,a3...

Question

If $a_{1}, a_{2}, a_{3}, . ., a_{n}, . .$ are in $A . P$ . Such that $a_{4} - a_{7} + a_{10} = m,$ then the sum of first $13$ terms of this $A . P$ ., is :

A

15 m

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B

10 m

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C

12 m

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D

13 m

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Solution

The correct option is B $13 m$
$a_{4} - a_{7} + a_{10} = m$

$\Rightarrow (a + 3 d) - (a + 6 d) + a + 9 d = m$

$\Rightarrow a + 3 d - a - 6 d + a + 9 d = m$

$\Rightarrow 6 d + a = m (1)$

$S_{13} = \frac{13}{2} (2 a + (13 - 1) d)$

$= \frac{13}{2} (2 a + 12 d)$

$= 13 (a + 6 d)$

$= 13 m$

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Similar questions

a_{1}, a_{2}, a_{3},

a_{n}

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a_{4} - a_{7} + a_{10} = m

, then sum of first

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a_{1}, a_{2}, a_{3}, . . . . . . . . .

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A . P

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are in A.P. such that

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terms of this A.P. is :

a_{1}, a_{2}, a_{3}, . . . .

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13^{t h}

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