Question

Alex decided to practice driving for a few days. On the first day he drove for only
increasing his journey by 4 miles each day. Calculate the total distance he travele
A. 358 miles in 12 days
B. 348 miles in 12 days
C. 335 miles in 10 days
D. O 338 miles in 15 days​

Answer 1

None of these.

Concept:

An arithmetic progression, also known as an arithmetic sequence, is a set of integers in which the difference between successive terms remains constant.

Given:

Each day Alex increases his journey by 4 miles.

Find:

The total distance traveled in 10 days, 12 days, and 15 days.

Solution:

As Alex increases his distance by 4 miles per day. Then, it forms an A.P as 4, 8, 12, 16...

The sum of the A.P of 12 terms is = $\frac{n}{2}[2a+(n-1)d]$

                                                       = $\frac{12}{2}[2*4+(12-1)*4]$

                                                       = $6[8+44]$

                                                       = 6*52

                                                       = 312 miles.

Hence, the option(A) and option (B) are incorrect.

The sum of the A.P of 10 terms = $\frac{10}{2}[2*4+(10-1)*4]$

                                                    = $5[8+36]$

                                                    = 220 miles.

Hence, option (C) is incorrect.

The sum of the A.P of 15 terms = $\frac{15}{2}[2*4+(15-1)*4]$

                                                    = $\frac{15}{2} [8+56]$

                                                    = $15*32$

                                                    = 480 miles.

Hence, option (D) is incorrect.