College

The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671, find:

a) The number of terms (n) in the AP.
b) The common difference between them.

Answer :

Final answer:

The number of terms (n) in the AP is 11 and the common difference is 12.

Explanation:

To find the number of terms (n) in the arithmetic progression (AP), we can use the formula for the sum of an AP: Sₙ = (n/2)(a + l), where Sₙ represents the cumulative total of a series, with 'a' denoting the initial term, 'l' indicating the final term, and 'n' signifying the number of terms. In this case, a = 1, l = 121, and Sₙ = 671. Plugging these values into the formula, we get: 671 = (n/2)(1 + 121). Simplifying this equation, we have: 671 = 61ₙ. When determining 'n,' we ascertain that it equals 11.

To find the common difference (d) between the terms, we can use the formula: d = (l - a)/(n - 1), where d is the common difference. Plugging in the values we already know, we have: d = (121 - 1)/(11 - 1), which simplifies to d = 12.

Learn more about Arithmetic Progression here:

https://brainly.com/question/30364336

#SPJ3

Answer:

(a)11

(b)12

Step-by-step explanation:

The first term, a = 1

The last term, l=121

Sum of the series, [tex]S_n=671[/tex]

Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:

[tex]S_n=\dfrac{n}{2}(a+l)[/tex]

Substituting the given values, we have:

[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]

(a)There are 11 terms in the arithmetic progression.

(b)We know that the 11th term is 121

The nth term of an arithmetic progression is derived using the formula:

[tex]a_n=a+(n-1)d[/tex]

[tex]a_{11}=121\\a=1\\n=11[/tex]

Therefore:

121=1+(11-1)d

121-1=10d

120=10d

d=12

The common difference between them​ is 12.