Question

PLEASE HELP! Find the general term of an arithmetic sequence that t6=15 and t11=-20. Hence, find the value of t17. No explanation is needed, just the working out. Will give medal :)

Answer 1

Use Use the general arithmetic sequence equation tn = t1 + (n-1)d
-where where d is the common difference for eac succesive term of the sequence
-where n describes the position of a term within a sequence

In your case we know that t6=15 and t11 = -20

Therefore,

t6=15=t1 + (6-1)d=t1 +5d ---> t1 = 15-5d

t11=-20= t1 + (11-1)d=t1 +10d---> t1 = -20-10d

Therefore,

15-5d=-20-10d--solve for d
d=-7

Now you can solve for t1 by plugging d into either of the t6 or t11 equation:

t11=-20=t1 + (10)(-7)--->t1 = 50

Now you can solve for t17

t17= t1 + (17-1)d= 50 + (16) (-7)=-62general arithmetic sequence equation tn = t1 + (n-1)d
-where where d is the common difference for eac succesive term of the sequence
-where n describes the position of a term within a sequence

In your case we know that t6=15 and t11 = -20

Therefore,

t6=15=t1 + (6-1)d=t1 +5d ---> t1 = 15-5d

t11=-20= t1 + (11-1)d=t1 +10d---> t1 = -20-10d

Therefore,

15-5d=-20-10d--solve for d
d=-7

Now you can solve for t1 by plugging d into either of the t6 or t11 equation:

t11=-20=t1 + (10)(-7)--->t1 = 50

Now you can solve for t17

t17= t1 + (17-1)d= 50 + (16) (-7)=-62

Answer 2

We hope this helps.


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