Question

if a=3 d=4 sn =406 find the value n​

Answer 1

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★ Given that,

• a = 3
• d = 4
• Sn = 406

★ To find,

• n = ?

By using sum of n terms of an AP...

☯ Sn = n/2 [ 2a + (n - 1)d ]

➡ 406 = n/2 [ 2(3) + (n - 1)4 ]

➡ 406 × 2 = n [ 6 + 4n - 4 ]

➡ 812 = n [ 2 + 4n ]

➡ 812 = 2n + 4n²

➡ 4n² + 2n - 812 = 0

➡ 2[2n² + n - 406 ] = 0

➡ 2n² + n - 406 = 0/2

➡ 2n² + n - 406 = 0

➡ 2n² + 29n - 28n - 406 = 0

➡ n(2n + 29) - 14(2n + 29) = 0

➡ (n - 14) (2n + 29) = 0

➡ n - 14 = 0 ; 2n + 29 = 0

➡ n = 0 + 14 ; 2n = 0 - 29

➡ n = 14 ; 2n = - 29

➡ n = 14 ; n = -29/2

Values of n can't be in fractions.So, n will be 14.

★ Verification :

Substitute the value of n in the formula.

➡ S14 = 14/2 [ 2(3) + (14 - 1)(4) ]

➡ S14 = 7 [ 6 + 13(4) ]

➡ S14 = 7 [ 6 + 52 ]

➡ S14 = 7 [ 58 ]

➡ S14 = 406.

Hence, it is verified...

$\underline{\boxed{\bf{\purple{∴ The\;number\;of\;terms\;are\;“\;14\;”.}}}}$

Step-by-step explanation:

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