The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49 1. Find the first

Question

The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n

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Thiên Thanh 3 years 2021-08-30T15:58:02+00:00 1 Answers 50 views 0

Answers ( )

  1. minhkhue
    0
    2021-08-30T15:59:56+00:00
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    Answer:

    For 1: The first term is 10 and the common difference is \frac{3}{2}

    For 2: The value of n is 27

    Step-by-step explanation:

    The n-th term of the progression is given as:

    a_n=a_1+(n-1)d

    where,

    a_1 is the first term, n is the number of terms and d is the common difference

    The sum of n-th terms of the progression is given as:

    S_n=\frac{n}{2}[2a_1+(n-1)d]

    where,

    S_n is the sum of nth terms

    • For (1):

    The 11th term of the progression:

    25=a_1+10d               …….(1)

    Sum of first 4 numbers:

    49=\frac{4}{2}[2a_1+3d              ……(2)

    Forming equations:

    98=8a_1+12d

    25=a_1+10d                  ( × 8)

    The equations become:

    98=8a_1+12d

    200=8a_1+80d

    Solving above equations, we get:

    102=68d\\\\d=\frac{102}{68}=\frac{3}{2}

    Putting value in equation (1):

    25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10

    Hence, the first term is 10 and the common difference is \frac{3}{2}

    • For 2:

    The nth term is given as:

    49=10+(n-1)\frac{3}{2}

    Solving the above equation:

    39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27

    Hence, the value of n is 27

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