Question

Given an arithmetic sequence with a7 = 19 and a12 = 54,

what is a65?

Answer 1

find first term and common difference at first

Answer 2

a7, a8, a9, a10, a11, a12.
Six terms, just subtract the difference.

Answer 3

\[54 - 19 \over 6 \]Divide by 6 as there are 6 terms to find the common difference.

Answer 4

make two equations from the given

Answer 5

Oh wait. Divide by 5.

Answer 6

7?

Answer 7

Yes. That makes the common difference for ya.

Answer 8

@ParthKohli that approcah is little difficult.....I mean confusing

Answer 9

\[a_n = a_1 +(n - 1)d \]

Answer 10

so i multiply 7 * 64?

Answer 11

Yeah yeah!

Answer 12

@sauravshakya Not to mind when the asker understands it :P

Answer 13

so the answer is 448?

Answer 14

Ya.

Answer 15

thanks for the help!

Answer 16

Wait no

Answer 17

First you have to find a1.

Answer 18

a7 = 19
a6 = 19 - 7
a5 = 19 - 7 - 7
a4 = 19 - 7 - 7 - 7
a3 = 19 - 7 - 7 - 7 - 7
a2 = 19 - 7 - 7 - 7 - 7 - 7
a1 = 19 - 7 - 7- 7 - 7 - 7 - 7

a1 = 19 - (7 * 6)

Answer 19

That makes a beautiful drawing of a sail :)

Answer 20

-23 and then i * 64

Answer 21

haha^^

Answer 22

\[a_{65} = -23 + 7(65 - 1) \implies -23 + (7 \times 64) \implies -23 + 448 \]

Answer 23

i think it is easier if u just
so u can find a1 and d and then replace at a65=a1+(65-1)d