Question

Последовательность (сn) задана условиями: с1 = 2 и сn = cn-1 + 2 при n>1. Найти с12.​

Answer 1

$\displaystyle\bf\\c_{1} =2\\\\c_{n} =c_{n-1} +2\\\\c_{2} =c_{1} +2=2+2=4\\\\c_{2} =c_{1} +d\\\\d=c_{2} -c_{1} =4-2=2\\\\c_{12}=c_{1} +11d=2+11\cdot 2=2+22=24\\\\Otvet:c_{12} =24$

Answer 2

Finding the 12th term of the sequence

The sequence is defined by the following conditions: c1 = 2 and cn = cn-1 + 2 for n > 1. We need to find the 12th term, c12.

To find the 12th term, we can use the recursive formula given in the conditions. Starting with c1 = 2, we can calculate each subsequent term until we reach c12.

Let's calculate the terms step by step:

c1 = 2 c2 = c1 + 2 = 2 + 2 = 4 c3 = c2 + 2 = 4 + 2 = 6 c4 = c3 + 2 = 6 + 2 = 8 c5 = c4 + 2 = 8 + 2 = 10 c6 = c5 + 2 = 10 + 2 = 12 c7 = c6 + 2 = 12 + 2 = 14 c8 = c7 + 2 = 14 + 2 = 16 c9 = c8 + 2 = 16 + 2 = 18 c10 = c9 + 2 = 18 + 2 = 20 c11 = c10 + 2 = 20 + 2 = 22 c12 = c11 + 2 = 22 + 2 = 24

Therefore, the 12th term of the sequence is 24.