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The first, second and last term of an arithmetic progression are respectively 4, 7 and 31. How many terms are there in the given arithmetic progression?
- a)14
- b)10
- c)9
- d)11
Correct answer is option 'B'. Can you explain this answer?
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The first, second and last term of an arithmetic progression are respe...
Given information:
The first term of the arithmetic progression (AP) is 4.
The second term of the AP is 7.
The last term of the AP is 31.
Approach:
To find the number of terms in the given AP, we can use the formula for the nth term of an AP:
an = a + (n-1)d
where a is the first term, n is the number of terms, and d is the common difference.
We are given the values of the first term, second term, and last term. Using these values, we can calculate the common difference, and then find the number of terms using the formula.
Solution:
Step 1: Calculate the common difference (d)
Given: First term (a) = 4, Second term = 7
Using the formula: a2 = a1 + d
7 = 4 + d
d = 7 - 4
d = 3
Step 2: Calculate the number of terms (n)
Given: First term (a) = 4, Last term (an) = 31, Common difference (d) = 3
Using the formula: an = a + (n-1)d
31 = 4 + (n-1)3
31 = 4 + 3n - 3
31 - 4 + 3 = 3n
30 = 3n
n = 30 / 3
n = 10
Therefore, there are 10 terms in the given arithmetic progression.
Answer:
The number of terms in the given arithmetic progression is 10 (option B).
The first term of the arithmetic progression (AP) is 4.
The second term of the AP is 7.
The last term of the AP is 31.
Approach:
To find the number of terms in the given AP, we can use the formula for the nth term of an AP:
an = a + (n-1)d
where a is the first term, n is the number of terms, and d is the common difference.
We are given the values of the first term, second term, and last term. Using these values, we can calculate the common difference, and then find the number of terms using the formula.
Solution:
Step 1: Calculate the common difference (d)
Given: First term (a) = 4, Second term = 7
Using the formula: a2 = a1 + d
7 = 4 + d
d = 7 - 4
d = 3
Step 2: Calculate the number of terms (n)
Given: First term (a) = 4, Last term (an) = 31, Common difference (d) = 3
Using the formula: an = a + (n-1)d
31 = 4 + (n-1)3
31 = 4 + 3n - 3
31 - 4 + 3 = 3n
30 = 3n
n = 30 / 3
n = 10
Therefore, there are 10 terms in the given arithmetic progression.
Answer:
The number of terms in the given arithmetic progression is 10 (option B).
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Community Answer
The first, second and last term of an arithmetic progression are respe...
a = 4, d = 7 - 4 = 3, tn = 31
∴ tn = a + (n - 1)d
⇒ 31 = 4 + (n - 1) 3
⇒
⇒ n - 1 = 9 ⇒ n = 10
∴ tn = a + (n - 1)d
⇒ 31 = 4 + (n - 1) 3
⇒
⇒ n - 1 = 9 ⇒ n = 10
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