Let a 1 , a 2 , a 3 , … … , a 49 be in A . P . such that Σ k ⁡ = 0 1 2 a 4 k + 1 = 416 and a 9 + a 43 = 66 . If a 1 2 + a 2 2 + … + a 17 2 = 140 m , then m is equal to:

Question

Let a 1 , a 2 , a 3 , &#8230; &#8230; , a 49 be in A . P . such that &#931; k &#8289; = 0 1 2 a 4 k + 1 = 416 and a 9 + a 43 = 66 . If a 1 2 + a 2 2 + &#8230; + a 17 2 = 140 m , then m is equal to:

Quantrex Academy · Accepted Answer

Correct answer: D. 34

a 1 + a 5 + &#160; . &#160; . &#160; . &#160; + a 49 = 416 Let common difference = &#160; d 13 a 1 &#160; + 4 d 1 + 2 + &#160; . &#160; . &#160; . &#160; + 12 = 416 13 a 1 &#160; + 4 d 12 13 2 = 416 13 a 1 &#160; + 24 d 13 = 416 a 1 + 24 d = 32 . &#160; . &#160; . &#160; ( i ) a 9 + a 43 = 66 a 1 + 8 d + a 1 + 42 d = 66 2 a 1 + 50 d = 66 a 1 + 25 d = 33 . &#160; . &#160; . &#160; ( i i ) a 1 = 8 &#160; &#160; &#160; ; &#160; &#160; d = 1 &#8721; i = 1 17 a i 2 = 140 m &#8658; a 2 + a + d 2 + &#160; . . &#160; .

Let a 1 , a 2 , a 3 , … … , a 49 be in A . P . such that Σ k ⁡ = 0 1 2 a 4 k + 1 = 416 and a 9 + a 43 = 66 . If a 1 2 + a 2 2 + … + a 17 2 = 140 m , then m is equal to:

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Correct answer

Step-by-step solution

More from Sequences and Series

Let a 1 , a 2 , a 3 , &#8230; &#8230; , a 49 be in A . P . such that &#931; k &#8289; = 0 1 2 a 4 k + 1 = 416 and a 9 + a 43 = 66 . If a 1 2 + a 2 2 + &#8230; + a 17 2 = 140 m , then m is equal to:

Options

Correct answer

Step-by-step solution

More from Sequences and Series

Let a 1 , a 2 , a 3 , … … , a 49 be in A . P . such that Σ k ⁡ = 0 1 2 a 4 k + 1 = 416 and a 9 + a 43 = 66 . If a 1 2 + a 2 2 + … + a 17 2 = 140 m , then m is equal to: