Question

Prove that the 5th term of AP is zero whose 12 the term & 19th terms are 16 & 32 respectively

Answer 1

tx is the xth term of the ap
$t12 = a + 11d = 16 \\ t19 = a + 18d = 32 \\ 18d - 11d = 7d = 16 \\ d = \frac{16}{7} \\ t5 = t12 - 7d = 16 - 16 = 0$
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