the 7th and 12th term of an AP are 34 and 59 respectively. find the first term of the AP, its common difference and it 21st term.
Answers
Step-by-step explanation:
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Answer:
Therefore, the 21st term of the AP is 104.
Step-by-step explanation:
Let the first term of the AP be 'a' and the common difference be 'd'. Then, the 7th term of the AP is a+6d and the 12th term is a+11d.
Given that the 7th term is 34, we have:
a+6d = 34 ...(1)
Also, given that the 12th term is 59, we have:
a+11d = 59 ...(2)
To find the first term of the AP and its common difference, we can solve these two equations simultaneously.
Subtracting equation (1) from equation (2), we get:
5d = 25
d = 5
Substituting d=5 in equation (1), we get:
a+6d = 34
a+6(5) = 34
a+30 = 34
a = 4
Therefore, the first term of the AP is 4 and the common difference is 5.
To find the 21st term, we can use the formula:
tn = a + (n-1)d
where tn is the nth term of the AP, n is the term number, a is the first term, and d is the common difference.
Substituting n=21, a=4, and d=5 in the formula, we get:
t21 = 4 + (21-1)5
t21 = 4 + 100
t21 = 104
Therefore, the 21st term of the AP is 104.
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