The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.

Question

qqstory · Answer

what is al?

qqstory · Answer

al The third term?

cwtan · Answer

a+2d=9
a+6d=31
solve a and d.

Sum of first nth term=
(n/2)(2a+(n-1)d)

sub the value inside and u will found the answer

anonymous · Answer

thats not supossed to be there

amistre64 · Answer

7-3 = 4

the difference between the 7th and 3rd terms is: 31-9 = 22

22/4 = the common difference, if i did that right :)

qqstory · Answer

22/4= 5.5. wrong, the third term is 9.

cwtan · Answer

1st term is -2?

amistre64 · Answer

9 + 4(22/4) = 31,  well, is does pan out

3: 9
4: 36/4 + 22/4 = 58/4
5: 58/4 + 22/4 = 80/4
6: 80/4 + 22/4 = 102/4
7: 102/4 + 22/4 = 124/4 = 31

amistre64 · Answer

an = a1 + d(n-1)

a3 = a1 + 22/4 (3-1)

9 - 22/2 = a1 = -2

a31 = -2 + 22/4 (30)

the sum of the terms is then:

$$\frac{31(-2-2+\frac{22*30}{4})}{2}$$

amistre64 · Answer

why did i read 22 as 31?

amistre64 · Answer

simple enough change :)

$$\frac{22(-2-2+\frac{22*21}{4})}{2}$$

cwtan · Answer

haha

amistre64 · Answer

i learnt something new today that im bound to forget by tomorrow; its something about arithmetic means between 2 numbers ....