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a) The nth term of a sequence is given as 3^{(m + 1)} - 2m.

a) The nth term of a sequence is given as 3^{(m + 1)} - 2m. Find the 5th term of the sequence
b) Atieno was employed by NGO on contract for a certain number of years. Her basic annual salary for the first year was sh 580 000 and her last basic annual salary was sh 630 400. By end of contract she had earned a total basic salary of sh 4 841 600. If the annual increment was constant, calculate
i) The period of the contract
ii) The annual increment
iii) The annual basic salary in the third year of contract

Answers

a) n^th term = 3^{m + 1} - 2m

5^th term = 3^{5 + 1-} 2(5)

= 3⁶ - 10 = 729 - 10 = 719

b) (i) a = 580 000

n^th term = 630, 400

580 000 + (n -1)d

= 630, 400

(n - 1)d

= 630 400 - 580 000

(n -1)d = 50 400

S_n = $\frac{n}{2}(2a \; +\;(n - 1)d)$

4 841 600 = $\frac{n}{2}(2a + 50 400)$

= $\frac{n}{2}(2a + 50 400)$

n = period of contract

= 8 years

ii) Annual increment

(n - 1)d = 50 400

(8 - 1)d = 50 400

7d = 50 400

d = 7 200

iii) Annual basic salary

in the third year

580 000 + (3 - 1)7 200

= 580 000 + 14 400

= sh 594 400

---

johnmulu answered the question on March 7, 2017 at 13:30

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