Question

in an A.P if first term is 4, 9th term is 20, then 15th term is

Answer 1

The 15th term of the ap is 32

Given

• first term is 4
• 9th term is 20

To find

• 15th term

Solution

we are provided with arithmetic progression whose first term is for and 9 the term is 20 and asked to find the 15 the term of the same AP.

First let ud find the common difference of the arithmetic progression and then we would use the standard equation to find the 15 the term.

a = 4

9th term is 20

or, 20 = 4 + 8d

or, 16 = 8d

or, d = 2

love letters find the 15th the term of the AP

a = 4

d = 2

an = a + (n-1)d

or, a_15 = 4 + (15-1)2

or, a_15 = 4 + 14×2

or, a_15 = 4 + 28

or, a_15 = 32

Therefore, the 15th term of the ap is 32

Answer 2

In an A.P if first term is 4, 9th term is 20, then 15th term is 32.

Arithmetic Progression (AP)

Arithmetic Progression (AP) is a chain of numbers in order, wherein the distinction among any  consecutive numbers is a steady value. It is likewise referred to as Arithmetic Sequence.

Notation in Arithmetic Progression

In AP, we will come across some main terms, which are denoted as:

• First term (a)
• Common difference (d)
• nth Term $\left(a_{n}\right)$
• Sum of the first $nterms (Sn)$

All three terms represent the property of Arithmetic Progression. We will learn more about these three properties in the next section.

First Term of AP

The AP can also be written in terms of common differences, as follows;

$a, a+d, a+2 d, a+3 d, a+4 d, \ldots \ldots \ldots, a+(n-1) d$

nth Term of an AP

The formula for finding the $n$-th term of an AP is:

$a_{n}=a+(n-1) \times d$

Given : 9th term is 20 , first term a = 4

STEP BY STEP SOLUTION

20 = 4 + (9-1)d

20-4 = 8d

$\frac{16}{8}$     = d

   2  = d

then 15th term will be

$a_{15}=4+(15-1) \times 2$

$a_{15}=32$

Thus, In an A.P if first term is 4, 9th term is 20, then 15th term is 32.

Learn more about Arithmetic Progression here,

https://brainly.in/question/4219484?msp_poc_exp=1

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