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2 answers:
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<u>Answer:</u>
<u>For 1:</u> The first term is 10 and the common difference is
<u>For 2:</u> The value of n is 27
<u>Step-by-step explanation:</u>
The n-th term of the progression is given as:
where,
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:
where,
is the sum of nth terms
- <u>For (1):</u>
The 11th term of the progression:
.......(1)
Sum of first 4 numbers:
......(2)
Forming equations:
( × 8)
The equations become:
Solving above equations, we get:
Putting value in equation (1):
Hence, the first term is 10 and the common difference is
- <u>For 2:</u>
The nth term is given as:
Solving the above equation:
Hence, the value of n is 27