Question

If for an A.P.
i) S₁₆ = 784, a = 4, find d.
ii) S₁₂ = -78, d = -3, find a .

Answer 1

(i) S16=784
a=4
$s16 = \frac{16}{2} (2 \times 4 + (16 - 1)d) \\ 784 = 8(8 + 15d) \\ 98 = 8 + 15d \\ 90 = 15d \\ \huge \bold{16 = d}$
(ii)S12=-78
d=-3

$s12 = \frac{12}{2} (2a + (12 - 1) - 3) \\ - 78 = 6(2a + 11( - 3) \\ - 13 = 2a - 33 \\ - 13 + 33 = 2a \\ 20 = 2a \\ \huge\bold{a = 10}$

Answer 2

Answer:

Step-by-step explanation

For the first bit d=6