Question

Sum of first 55 terms in an A.P. is 3300, find its 28th term. Solve the word problem

Answer 1

Answer:

60

Step-by-step explanation:

sum of 55 terms =3300

55/2(2a+54d)= 3300

2a+54d=3300x2/5

2a+54d=120

divide both sides by 2

a+27d=60. (1)

Now 28th term=a+27d by formula. (2)

by (1) and (2)

28th term of ap =60

Answer 2

Answer:-

$\boxed{ \bf{t_{28} = 60}}$

Step - by - step explanation :-

To find :-

Find 28th term of the given AP.

Given :-

55th term is 3300.

Solution:-

Let first term of this AP is "a"

Common difference is "d"

According to the question-

$\: \bf{s_{55} = 3300} \\ \\ \bf{ \frac{55}{2} \bigg(2a + (55 - 1)d \bigg) = 3300} \\ \\ \bf{\frac{55}{2} \bigg(2a + 54d \bigg) = 3300} \\ \\ \bf{ 55(a + 27d) = 3300} \\ \\ \bf{a + 27d \: = 60 }\: \: \: ......(1)$

And also ,

We know that,

$\bf{t_{28} \: = a \: + (28 - 1)d} \\ \\ \bf{ t_{28} \: = a + 27d \: } \: ......(2)$

On comparing eq (1) and (2)

We get,

$\boxed{ \red{\bf{t_{28} = 60}}}$

Hope it helps you.