Math, asked by rayaanlone, 10 months ago

An arithmetic sequence has a 2nd term equal to 7 and 8th term equal to -23. Find the term of the sequence that has value -183

Answers

Answered by Slogman
0

Given:

a2 = 7

a8 = -23

an = -183

To find:

Term of the sequence that has value -183.

Solution:

Since, a2 = 7

=> a+(2-1)d = 7

=> a+d = 7 ---------------(1)

Also, given a8 = -23

=> a+(8-1)d = -23

=> a+7d = -23

Now, from (1) We get

a = 7-d ----------------(2)

Putting the value of a in the above equation

We get, (7-d)+7d = -23

=> 7-d+7d = -23

=> 7+6d = -23

=> 6d = -23-7

=> 6d = -30

=> d = -30/6

=> d = -5

Now, putting the value of d in equation (2)

We get, a = 7-(-5)

=> a = 7+5

=> a = 12

Now, an = -183

=> a+(n-1)d = -183

Putting values, We get

12+(n-1)(-5) = -183

=> -5n+5 = -183-12

=> -5n+5 = -195

=> -5n = -195-5

=> -5n = -200

=> n = -200/-5

=> n = 40

Hence, the 40th term of the given A.P. is -183.

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