Question

The sum of the arithmetic progression 4, ..., 76 is 1920. Find the number of terms and the common difference.​

Answer 1

Number of terms = 48

common difference = 1.5

This question involves the concept of Arithmetic Progression.

• The formula for sum of an arithmetic progression series with first and last term given is;

$S_{n}$ = $\frac{n}{2}$(a + l)

where;

a = first term

l = last term

n = number of terms

• From the given sequence, we see that;

first term; a = 4

last term; l = 76

Sum of A.P; $S_{n}$ = 1920

• Plugging in relevant values into the sum of an AP formula, we have;

1920 = $\frac{n}{2}$(4 + 76)

simplifying this gives;

1920 = 40n

n = 1920/40

n = 48

• Formula for nth term of an AP is;

$t_{n}$ = $a_{1}$ + (n - 1)d

where;

$a_{1}$ is first term

d is common difference

n is number of term

$t_{n}$ is the nth term in question

the 48th term is 76

Thus;

76 = 4 + (48 - 1)d

76 - 4 = 47d

72 = 47d

d = 72/47

d ≈ 1.5

Thus;

Number of terms = 48

common difference = 1.5

Read more at; brainly.com/question/16935540