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## 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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Mathematics
3 years
2021-08-30T15:58:02+00:00
2021-08-30T15:58:02+00:00 1 Answers
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## Answers ( )

Answer:For 1:The first term is 10 and the common difference isFor 2:The value of n is 27Step-by-step explanation: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

For (1):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 isFor 2:The nth term is given as:Solving the above equation:Hence, the value of n is 27