Question

The sum of the first four terms of an arithmetic progression is 56 and the sum of the last four terms is 112. If its first term is 11, then the number of terms is

Answer 1

Answer:

The number of terms = 11

Step-by-step explanation:

Given :

• The sum of the first four terms of an arithmetic progression is 56
• The sum of the last four terms is 112.
• The first term is 11

To find :

the number of terms

Solution :

first term, a = 11

nth term of an AP is given by,

$\longrightarrow \tt a_n=a+(n-1)d$

Let the Arithmetic Progression be

a, a+d, a+2d, a+3d, .... a+(n-2)d, a+(n-1)d

Sum of first four terms = 56

a + a+d + a+2d + a+3d = 56

4a + 6d = 56

4(11) + 6d = 56

44 + 6d = 56

6d = 56 – 44

6d = 12

d = 12/6

d = 2

Common difference, d = 2

Sum of last four terms = 112

[a+(n−4)d] + [a+(n−3)d] + [a+(n−2)d] + [a+(n−1)d] = 112

a + nd – 4d + a + nd – 3d + a + nd – 2d + a + nd – d = 112

4a + 4nd – 10d = 112

4(11) + 4n(2) – 10(2) = 112

44 + 8n – 20 = 112

8n + 24 = 112

8n = 112 – 24

8n = 88

n = 88/8

n = 11

Therefore, the number of terms = 11

Answer 2

Step-by-step explanation:

snehitha answer ✌️✌️

ghtyydtdfgtdggfgh.... yt7gjm. hgjmmu