Question

An arithmetic series a consists of consecutive integers that are multiples of 4 what is the sum of the first 9 terms of this sequence if the first term is 0

Answer 1

Answer: 144

Step-by-step explanation:

Since, the first 9 multiple of 4 starts from 0 are,

0, 4, 8, 12, 16, 20, ................

Which is an AP,

Having the first term, $a_1 = 0$

And, the successive difference, d = 4,

Since, the sum of the n term of an AP,

$S_n = \frac{n}{2}[2a + (n-1)d]$

Hence the sum of 9 term of the above AP,

$S_9 = \frac{9}{2}[2\times 0 + (9-1)\times 4]$

$S_9 = \frac{9}{2}(0 + 8\times 4)$

$S_9 = \frac{9}{2}(32)$

$S_9 = \frac{288}{2}=144$