Here are the first four tearms of a sequence 1, 11, 22, 37, find and express in terms of n the nth term of this sequence

2n² + n + 1

Explanation:

The sequence is 4, 11, 22, 37

Difference between:  7, 11, 15

The first differences are 7, 11, 15, and the second differences are 4.

Since half of 4 is 2, then the first term will be 2n^2.

Subtracting 2n² from the sequence gives 2, 3, 4, 5 which has nth term n + 1.

Therefore the final answer is 2n² + n + 1

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.