Question

A student taking a test consisting of 10 questions is told that each questions after the first is worth 2 marks more than the preceding question. If the third question of the test is worth 5 marks.What is the maximum score that the student can obtain by attempting?

Answer 1

Answer:

Student can obtain 15 marks by attempting 8 questions.

Step-by-step explanation:

This question is incomplete; complete question is here.

A student taking a test consisting of 10 questions is told that each questions after the first is worth 2 marks more than the preceding question. If the third question of the test is worth 5 marks.What is the maximum score that the student can obtain by attempting 8 questions?

A students when attempts the questions the sequence formed by the scores he gets will be in the form of a, (a + 2), (a + 4), (a + 6)........

Which will be an arithmetic sequence with a common difference = 2

We know explicit formula of an arithmetic sequence is

$T_{n}=a+(n-1)d$

Where $T_{n}$ = First term of the sequence

a = first term

n = number of term

d = common difference

It is given that 3rd term of this sequence is 5.

$5=a+(3-1)2$

a = 5 - 4 = 1

Explicit formula for the sequence will be $T_{n}=1+(n-1)2$

$T_{n}=2n-1$

Now if the student attempts 8 questions then from the explicit formula

$T_{8}=8\times 2-1$

$T_{8}=15$

Therefore, student can obtain 15 marks by attempting 8 questions.