If the third term of an AP is 12 and 16th term is 77, find the AP.
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If the third term of an AP is 12 and 16th term is 77, find the AP.
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Question:-
➡ If the third term of an AP is 12 and the 16th term is 77, find the AP
Answer:-
➡ The given AP will be,
2 7 12 17 22....
Solution:-
Given that,
➡ 3rd term of AP is 12.
➡ 16th term of AP is 77
Let us assume that, first term of the AP is a and the common difference be d.
So,
3rd term of the AP = a + (3-1)d
➡ 3rd term = a + 2d
➡ a + 2d = 12 ......... (i)
Also,
16th term of the AP = a + (16-1)d
➡ 16th term = a + 15d
➡ a + 15d = 77 ....... (ii)
Now, subtracting equation (i) from (ii), we get,
➡ a + 15d - (a + 2d) = 77 - 12
➡ a + 15d - a - 2d = 65
➡ 13d = 65
➡ d = 5 (Keep it in mind)
Hence, the common difference we get here is 5.
Now, substituting d in equation (i), we get,
➡ a + 2×5 = 12
➡ a + 10 = 12
➡ a = 2 (Remember)
Hence, the first term of the AP is 2.
So,
Second Term=2+5=7
Third Term = 7+5 = 12
Fourth Term = 12+5 = 17 and so on.
Hence, the AP will be,
2 7 12 17 22...