Q3 of 67 Page 69

The sixth term and the 17th term of the arithmetic progression are 19 and 41 respectively. Then find the 40th term.

Let first term be a and common difference be d.
We know that, an = a + (n - 1)d
 ∴ a6 = a + (6 - 1)d
⇒ 19 = a + 5d …(i)
and a17 = a + (17 - 1)d
⇒ 41 = a + 16d …(ii)


On solving eq. (i) and (ii), we get,
a = 9 and d = 2


⇒ a40 = a + (40 - 1)d
⇒ a40 = 9 + (40 - 1) × 2
⇒ a40 = 9 + 39× 2 = 9 + 78 = 87


Hence, 40th term is 87.


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