Question

in an ap sum of the first 11 terms is 44 and the sum of next 11 terms is 55 find the ap

Answer 1

Given
S11 = 44
S 23 = 55

Now S 11 = 11/2 (2a + 10d) = 44
= 2a + 10d = 88/11
= a + 5d = 8. ..... eq 1
S23 = 22/2 (2a+ 21d) = 55
= 2a + 21d = 110/22
= 2a + 21d = 5. ......eq 2

solving eq 1 and 2
d = -1 and a = 13

Answer 2

Answer:

a= 39/11 and d= 1/11

Step-by-step explanation:

Formula of the sum is,

S= (1/2)n(a+1)

where n is the nth term, a is the first term, d is the common difference.

Using formula for n=11 we get,

S=(1/2)11(a+1)d

Implies, S=44,therefore,

44=(1/2)11(a+1)d

gives,

2a+10d= 8

Using the same formula for n=22,

S=(1/2)22(2a+(22-1)d)

gives,

2a+21d=9

Solving both the equations we get,

11d=1

implies,

d=1/11

Substituting value of d we get,

Substituting value of d we get,a= 11/39

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