Question

If a13 = 51 and d = 4, what is S13​

Answer 1

$Given \: in \: an \: A.P : a_{13} = 51 \:and \:d=4$

/* We know that */

$\boxed{\pink{ n^{th} \:term \:(a_{n}) = a+(n-1)d}}$

$i ) a_{13} = 51$

$\implies a + ( 13 - 1 )\times 4 = 51$

$\implies a + 12 \times 4 = 51$

$\implies a + 48 = 51$

$\implies a = 51 - 48$

$\implies a = 3$

/* We know that */

$\boxed{\blue{ Sum \:of \: n\: terms (S_{n})= \frac{n}{2}[2a + (n-1)d ]}}$

$Here, a = 3, d = 4 \:and \: n = 13$

$\red{ S_{13} }\\= \frac{13}{2}[ 2 \times 3 + ( 13 - 1) \times 4 ] \\= \frac{13}{2}[ 6 + 12 \times 4 ] \\= \frac{13}{2} [ 6 + 48 ]\\= \frac{13}{2} \times 54 \\= 13 \times 27 \\= 351$

Therefore.,

$\red{ S_{13}} \green { = 351}$

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