We appreciate your visit to If the nth term of the arithmetic progression AP 3 10 17 is the same as the nth term of the AP 63 65 67. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer:
n = 13
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
[tex]a_{n}[/tex] = 3 + 7(n - 1) (for the first AP)
[tex]a_{n}[/tex] = 63 + 2(n - 1) ( for the second one)
3 + 7(n - 1) = 63 + 2(n - 1)
3 + 7n - 7 = 63 + 2n - 2
5n = 65
n = 13
Thanks for taking the time to read If the nth term of the arithmetic progression AP 3 10 17 is the same as the nth term of the AP 63 65 67. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Answer:
n = 13
Step-by-step explanation:
AP = 2, 10, 17 ...
AP1 = 63,65, 67
Find the general term of AP
L = a + (n - 1)*d
a = 2
d = 7
Find the general term of AP1
L = 63 + (n - 1)*d
a = 63
d = 2
Equation to equate both of them
L = 3 + (n-1)7
L1 = 63 + (n - 1)*2
Equate L and L1
2 + (n - 1)*7= 63 + (n-1)*2 Subtract 3 from both sides
(n - 1)*7 = 63 - 3 + (n - 1)*2 Remove the brackets
7n - 7 = 60 + 2n - 2 Combine the like terms on the right
7n - 7 = 58 + 2n Subtract 2n from both sides
7n - 2n -7 = 58 Add 7 to both sides
5n = 58 +7 Divide by 5
n = 65/5
n = 13
So the 13th term on each series is equal.
L_13 = 3 + (13 - 1)*7
L_13 = 3 + (12)*7
L_13 = 87
=====================
L'_13 = 63 + (13 -1 ) * 2
L'_13 = 63 + 12*2
L'_13 = 87
