Question

Find the 20th term arthmetic sequence it's 6th termis 14th term is 6

Answer 1

Answer:

Let say

first term: a1

20th term: a20

40th term: a40

nth term: an

and let say the series increases by x (a2=a1+x, …, an=a1+(n-1)x)

Then,

a20=a1+19x =14 (1)

a40=a1+39x =-6 (2)

substract (1) from (2),

a40-a20=(-6)–14=-20=20x

Then, x=-1.

So the sequence decreases by 1 ( like 6–5–4…)

Now, lets find the first term a1.

From (1), a1=14+19=33

the 10th term: a10=a1+9x

a10=33+9(-1)=24.