-2
$\begingroup$

given an arithmetic progression that T(14)=-8 and T(20)=-20, find the 50th term of the progression.

$\endgroup$

closed as off-topic by JonMark Perry, Xander Henderson, user99914, Leucippus, Claude Leibovici Dec 22 '17 at 6:52

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – JonMark Perry, Xander Henderson, Community, Leucippus, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ $6$ seconds later you find yourself $12$ steps down the stairs. Then after $36$ seconds $\cdots$ $\endgroup$ – dxiv Dec 22 '17 at 4:41
1
$\begingroup$

HINT: $T(50)=T(20)+5(T(20)-T(14))$. You do not need to find $a$ and $d$ for this part of your question.

$\endgroup$
0
$\begingroup$

Pointers:

  • The $n^{\text{th}}$ term of an Arithmetic progression with starting term $a$ and common difference $d$ is: $$T_n = a + (n-1)d$$

  • Given: $T_{14}$ and $T_{20}$, can you solve the two equations to get $a$ and $d$?

$\endgroup$
0
$\begingroup$

Since there is always a constant difference "d" in an arithmetic progression, it doesn't matter where you begin. To make things easier, let's imagine a sequence that goes from the 14th to the 20th term of your sequence. So a(1)=T(14). This means that T(20) would be a(7) (since 20 is 6 more than 14 and 7 is 6 more than 1). We can now rewrite your problem as:

a(1)=-8 and a(7)=-20. Find the common difference.

a(n)=a(1)+(n-1)d a(6)=a(1)+(7-1)d -20=-8+6d -12=6d d=-2

Since a(1)=T(14) then T(50)=a(37) (since 50 is 36 more than 14 and 37 is 36 more than 1).

a(n)=a(1)+(n-1)d a(37)=a(1)+(37-1)d a(37)=-8+(37-1)(-2) a(37)=-8+(36)(-2) a(37)=-8+-72 a(37)=-80

This is T(50)

$\endgroup$
  • $\begingroup$ Hi, thank you for contributing your answer. In Math SE we use MathJax to format mathematical writing for readability. You can look up the tutorial in meta :) $\endgroup$ – Karn Watcharasupat Dec 22 '17 at 5:28

Not the answer you're looking for? Browse other questions tagged or ask your own question.