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Determine the A.P. Whose Third Term is 16 and 7th Term Exceeds the 5th by 12. - Mathematics

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Sum

Determine the A.P. whose third term is 16 and 7th term exceeds the 5th by 12.

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Solution

Given:

3rd term of the AP is 16.
a3 = 16
a + (3 − 1)d = 16
a + 2d = 16                      .....(1)
Also, 7th term exceeds the 5th term by 12.
a7 − a5 = 12
[ a+ (7 − 1)d ] − [a + (5 − 1)d] = 12
(a + 6d) − (a + 4d) = 12
2d = 12
d = 6

From equation (1), we obtain
a + 2(6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be 4, 10, 16, 22, …

Concept: nth Term of an AP
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