Daya gets pocket money from his father every day. Out of the pocket money, he saves ₹ 2.75 on first day, ₹ 3.00 on second day, ₹ 3.25 on third day and so on. Find :

(i) the amount saved by Daya on 14^th day

(ii) the amount saved by Daya on 30^th day

(iii) the total amount saved by him in 30 days.

2.75, 3.00, 3.25, …………..

The above A.P. has first term (a) = 2.75 and common difference (d) = 3.00 - 2.75 = 0.25

By formula,

n^th term = a_n = a + (n - 1)d.

(i) The amount saved by Daya on 14^th day = 14th term of A.P.

a₁₄ = a + (14 - 1)d

= a + 13d

= 2.75 + 13 × 0.25

= 2.75 + 3.25

= ₹ 6.

Hence, the amount saved by Daya on 14^th day = ₹ 6.

(ii) The amount saved by Daya on 30^th day = 30th term of A.P.

a₃₀ = a + (30 - 1)d

= a + 29d

= 2.75 + 29 × 0.25

= 2.75 + 7.25

= ₹ 10.

Hence, the amount saved by Daya on 30^th day = ₹ 10.

(iii) Sum of A.P. = $\dfrac{n}{2}[2a + (n - 1)d]$

Total amount saved by Daya in 30 days = Sum of A.P. upto 30 terms.

$= \dfrac{30}{2}[2 \times 2.75 + (30 - 1) \times 0.25] \\[1em] = 15 \times [5.5 + 29 \times 0.25] \\[1em] = 15 \times [5.5 + 7.25] \\[1em] = 15 \times 12.75 \\[1em] = ₹ 191.25$

Hence, total amount saved by Daya in 30 days = ₹ 191.25