vince022503
11.01.2020 •
Mathematics
The product of 5 terms of a gp is
243. the 3rd term of gpis equal
to 10th term of ap.find sum of
19th term in arthematic series.
Solved
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Ответ:
The 19th term of Arithmetic series is - 2.02
Step-by-step explanation:
Given as :
The product of 5 terms of a GP = 243
The 3rd term of GP is = 10th term of AP
Let The sum of 19th term of AP = x
Now, According to question
∵ nth term of GP is given by
= a×
where a is the first term and n is nth term and r is the common ratio
So For n = 1
= a×
Or, = a×
i.e = a × 1
Or, = a
For n = 2
= a×
Or, = a×
i.e = a × r
For n =3
= a×
Or, = a×
i.e = a × r²
For n =4
= a×
Or, = a×
i.e = a × r³
For n =5
= a×
Or, = a×
i.e = a ×
Now, According to question
product of 5 terms of a GP = 243
So, × × × × = 243
Or, a × a r × a r²× a r³× a = 243
Or, × =
∴, a r² = 3 ............1
Again
3rd term of GP = 10th term of AP
∵ nth term for AP
Tn = a + (n - 1) r , where a is first term and r is common difference
So, 10th term of AP
= a + (10 - 1) r
= a + 9 r
∵ =
Or, a r² = a + 9 r
Now, from eq 1
3 = a + 9 r
i.e a + 9 r = 3
Or, + 9 r = 3
Or, 3 + 9 r³ = 3 r²
Or, 9 r³ - 3 r² + 3 = 0
Or, r = - 0.59
and a =
i.e a = 8.6
Now, 19th term of AP
= a + (19 - 1) r
= 8.6 + 18 × (-.59)
∴ = - 2.02
So, The 19th term of Arithmetic series = tex]A_19[/tex] = - 2.02
Hence, The 19th term of Arithmetic series is - 2.02 Answer
Ответ:
u take y2 - y1 and x2 -x1 so yeah take
7-7/7+3= 0/10 so the answer is y=0/10x
if your wondering how I got 7+3 it's because when u take a number and - it by another number that a negative it turns into a positive.
hope it helps