Page 7 - 11-Math-6 Sequences and Series

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Example 3: Find the number of terms in the A.P. if; a1 = 3, d = 7 and an =59.

Solution: Using an = a1 + (n - 1)d, we have
59 = 3 + (n - 1) % 7
(a an = 59, a1 = 3 and d = 7)

or 56 = (n - 1) % 7 ⇒ (n - 1) = 8 ⇒ n = 9

Thus the terms in the A.P. are 9.

Example 4: If an-2 = 3n - 11, find the nth term of the sequence.

Solution: Putting n = 3, 4, 5 in an-2 = 3n - 11, we have

a1 = 3 % 3 - 11 = -2
a2 = 3 % 4 - 11 = 1
a3 = 3 % 5 - 11 = 4
Thus an = a1 + (n - 1)d = -2 + (n - 1) % 3 (a a1 = -2, and d = 3)

= 3n - 5

Exercise 6.2

1. Write the first four terms of the following arithmetic sequences, if

i) a1 = 5 and other three consecutive terms are 23, 26, 29
ii) a5 = 17 and a9 = 37 iii) 3a7 = 7a4 and a10 = 33
2. If an-3 = 2n - 5, find the nth term of the sequence.
3. If the 5th term of an A.P. is 16 and the 20th term is 46, what is its 12th term?

4. Find the 13th term of the sequence x, 1, 2 - x, 3 - 2x,...

5. Find the 18th term of the A.P. if its 6th term is 19 and the 9th term is 31.

6. Which term of the A.P. 5, 2, -1,... is -85?

7. Which term of the A.P. -2, 4, 10,...is 148?

8. How many terms are there in the A.P. in which a1 =11 , an = 68, d = 3?
9. If the nth term of the A.P. is 3n - 1 , find the A.P.

10. Determine whether (i) -19, (ii) 2 are the terms of the A.P. 17, 13, 9, ... or not.

11. If l, m, n are the pth, qth and rth terms of an A.P., show that
i) l(q - r) + m(r - p) + n(p - q) = 0
ii) p(m - n) + q(n - l) + r(l - m) = 0

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