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Common Difference

Question 16De...

Question

Question 16
Determine the A.P. whose third term is 16 and the $7^{t h}$ term exceeds the $5^{t h}$ term by 12.

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Solution

$a_{3} = 16 a + (3 - 1) d = 16 a + 2 d = 16 \dots \dots (i) a_{7} - a_{5} = 12 [a + (7 - 1) d] - [a + (5 - 1) d] = 12 (a + 6 d) - (a + 4 d) = 12 2 d = 12 d = 6 F r o m e q u a t i o n (i), w e g e t, a + 2 (6) = 16 a + 12 = 16 a = 4 T h e r e f o r e, r e q u i r e d A . P i s,$
4, 10, 16, 22, …

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