Question

how to solve this problem

Answer 1

$given \: \\ a7 = 13 \\ \\ an = a + (n - 1)d \\ \\ a13 = a + 6d = 13......(1) \\ \\ s14 = 203 \\ \\ s14 = \frac{n}{2} (2a + (n - 1)d) \\ \\ s14 = \frac{14}{2} (2a + 13d) \\ \\ s14 = 14a + 91d = 203.......(2) \\ \\ by \: using \: \: elimination \: method \: \\ \\ a + 6d = 13...... \times 14 \\ \\ 14a + 91d = 203...... \times 1 \\ \\ on \: subtracting \: equation \: (1) - (2) \\ \\ we \: get \\ \\ - 7d = - 21 \\ \\ d = 3 \\ \\ by \: putting \: this \: value \: of \: d \: in \: equation \: (1) \\ \\ we \: get \\ \\ a + 18 = 13 \\ \\ a = - 5 \\ \\ now \\ \\ s8 = \frac{8}{2} (2a + 7d) \\ \\ s8 = 8a + 28d \\ \\ = 8( - 5) + 28(3) \\ \\ = - 40 + 84 \\ \\ = 44 \\ \\ thus \: s8 = 44 \\ \\ hope \: this \: helps \: you$
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