Question

if a=12,d=4 and S=672,Find number of terms​

Answer 1

Answer:

$your \: ans$

Step-by-step explanation:

$here \\ a = 12 \\ d = 4 \\ sn = 672 \\ \\ we \: know \: that \\ sn = \frac{n}{2} [2a + (n - 1)d] \\ \\ \implies672 = \frac{n}{2}[2 \times 12 + (n - 1) \times 4 ] \\ \\ \implies672 = \frac{n}{2} (24 + 4n - 4) \\ \\ \implies \: 672 \times 2 = 20n + {4n}^{2} \\ \\ \implies1344 = {4n}^{2} + 20n \\ \\ \implies {n}^{2} + 5n -336 = 0 \\ \\ \implies {n}^{2} + (21n - 16n) - 336 = 0 \\ \\ \implies {n}^{2} + 21n - 16n - 336 = 0 \\ \\ \implies \: n(n + 21) - 16(n + 21) = 0 \\ \\ \implies(n - 16)(n + 21) = 0 \\ \\ n = - 21( \times ) \: \: \: and \: n = 16$

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