Question

What is sum of 13 terms in ap whose 5th term is 1 and 8th term is -17?

Answer 1

Let the first term be 'a'
Common difference be 'd'
$t5 = 1 \\ a + (5 - 1)d = 1 \\ a + 4d = 1 - - - (1)$
$t8= - 17 \\ a + (8 - 1)d = - 17 \\ a + 7d = - 17 - - - (2)$
$(1) - (2) \: gives \\ - 3d = 18 \\ d = - 6 \\ from \: \: (1) \\ a + 4 \times - 6 = 1 \\ a = 25$

$s13 = \frac{13}{2} (2a + (13 - 1)d \\ = 13(a + 6d) \\ = 13 \times (25 + 6 \times - 6) \\ = 13 \times - 11 = - 143$