The best way for solving the problem of arithmetic progressions of exercise 5.2 of math. How i solve this question in easy way Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.
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Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12. Q.16
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Given,
Third term, a3 = 16
As we know,
a +(3−1)d = 16
a+2d = 16 ………………………………………. (i)
It is given that, 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 (i), we get,
a+2(6) = 16
a+12 = 16
a = 4
Therefore, A.P. will be4, 10, 16, 22, …