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If the 3rd and 7th terms of an arithmetic progression are 17 and 27 respectively. Find the first term of arithmetic progression.
- a)12
- b)14
- c)10
- d)8
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the 3rd and 7th terms of an arithmetic progression are 17 and 27 re...
Let a be the first term and d be the common difference
a + 2d = 17
a + 6d = 27
Solving these eqns we get a = 12
a + 2d = 17
a + 6d = 27
Solving these eqns we get a = 12
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Community Answer
If the 3rd and 7th terms of an arithmetic progression are 17 and 27 re...
To find the first term of an arithmetic progression, we need to determine the common difference (d) and use it to find the first term (a₁).
Given information:
- The 3rd term is 17
- The 7th term is 27
Step 1: Find the common difference (d)
The common difference (d) is the difference between any two consecutive terms in an arithmetic progression. We can use the formula for the general term (an) of an arithmetic progression to find the common difference.
The general formula for the nth term (an) of an arithmetic progression is:
an = a₁ + (n - 1)d
We can use this formula with the given information to set up two equations:
17 = a₁ + (3 - 1)d ...(1)
27 = a₁ + (7 - 1)d ...(2)
Step 2: Solve the equations
We now have a system of two equations with two unknowns (a₁ and d). We can solve this system of equations to find the values of a₁ and d.
Subtract equation (1) from equation (2) to eliminate a₁:
27 - 17 = (a₁ + (7 - 1)d) - (a₁ + (3 - 1)d)
10 = a₁ + 6d - a₁ - 2d
10 = 4d
Divide both sides of the equation by 4:
d = 10/4
d = 2.5
Step 3: Find the first term (a₁)
We can substitute the value of d into equation (1) or (2) to find the value of a₁.
Let's use equation (1):
17 = a₁ + (3 - 1)(2.5)
17 = a₁ + 2(2.5)
17 = a₁ + 5
a₁ = 17 - 5
a₁ = 12
Therefore, the first term of the arithmetic progression is 12.
Given information:
- The 3rd term is 17
- The 7th term is 27
Step 1: Find the common difference (d)
The common difference (d) is the difference between any two consecutive terms in an arithmetic progression. We can use the formula for the general term (an) of an arithmetic progression to find the common difference.
The general formula for the nth term (an) of an arithmetic progression is:
an = a₁ + (n - 1)d
We can use this formula with the given information to set up two equations:
17 = a₁ + (3 - 1)d ...(1)
27 = a₁ + (7 - 1)d ...(2)
Step 2: Solve the equations
We now have a system of two equations with two unknowns (a₁ and d). We can solve this system of equations to find the values of a₁ and d.
Subtract equation (1) from equation (2) to eliminate a₁:
27 - 17 = (a₁ + (7 - 1)d) - (a₁ + (3 - 1)d)
10 = a₁ + 6d - a₁ - 2d
10 = 4d
Divide both sides of the equation by 4:
d = 10/4
d = 2.5
Step 3: Find the first term (a₁)
We can substitute the value of d into equation (1) or (2) to find the value of a₁.
Let's use equation (1):
17 = a₁ + (3 - 1)(2.5)
17 = a₁ + 2(2.5)
17 = a₁ + 5
a₁ = 17 - 5
a₁ = 12
Therefore, the first term of the arithmetic progression is 12.
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If the 3rd and 7th terms of an arithmetic progression are 17 and 27 respectively. Find the first term of arithmetic progression.a)12b)14c)10d)8Correct answer is option 'A'. Can you explain this answer?
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