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The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find A. The first five term of the linear sequence. B. Sum of the first Nth of the exponential sequence C. The sum of the Nth term of linear sequence D. The limit of the sum of term for large value of N?
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The first and second term of an exponential sequence are respectively ...
Problem Statement

The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find:


  • A. The first five term of the linear sequence.

  • B. Sum of the first Nth of the exponential sequence.

  • C. The sum of the Nth term of linear sequence.

  • D. The limit of the sum of term for large value of N? Explain in details.



Solution

Given:


  • The first term of the exponential sequence is A.

  • The common ratio of the exponential sequence is r.

  • The first term of the linear sequence is a.

  • The common difference of the linear sequence is d.

  • The fourth term of the linear sequence is 10.

  • The sum of the first five terms of the linear sequence is 60.



Linear Sequence

Let's find the common difference (d) of the linear sequence:


  • The fourth term of the linear sequence is 10.

  • So, the fourth term can be written as a + 3d = 10.

  • Similarly, the sum of the first five terms of the linear sequence is 60.

  • So, (5/2)(2a+4d) = 60, which simplifies to a+2d = 12.

  • Now, we have two equations and two variables:


    • a + 3d = 10

    • a + 2d = 12


  • Solving the equations, we get a = 4 and d = 2.


So, the first five terms of the linear sequence are:


  • a = 4

  • a+d = 6

  • a+2d = 8

  • a+3d = 10

  • a+4d = 12



Exponential Sequence

Since the first and second terms of the exponential sequence are respectively the first and third term of the linear sequence, we have:


  • A = 4

  • ar = a+2d = 8


Dividing the second equation by the first equation, we get:


  • r = (a+2d)/a = 2


So, the common ratio of the exponential sequence is 2.

Now, we can find the sum of the first N terms of the exponential sequence using the formula:


  • Sn =
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The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find A. The first five term of the linear sequence. B. Sum of the first Nth of the exponential sequence C. The sum of the Nth term of linear sequence D. The limit of the sum of term for large value of N?
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The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find A. The first five term of the linear sequence. B. Sum of the first Nth of the exponential sequence C. The sum of the Nth term of linear sequence D. The limit of the sum of term for large value of N? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find A. The first five term of the linear sequence. B. Sum of the first Nth of the exponential sequence C. The sum of the Nth term of linear sequence D. The limit of the sum of term for large value of N? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and second term of an exponential sequence are respectively the first and third term of a linear sequence. The fourth term of the linear sequence is 10 and the sum of it's first five term is 60. Find A. The first five term of the linear sequence. B. Sum of the first Nth of the exponential sequence C. The sum of the Nth term of linear sequence D. The limit of the sum of term for large value of N?.
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