Question

the fifth term of an ap is 20.the sum of fifth and seventh terms of the ap is 64.find the common difference.

Answer 1

Answer:

d = 12

Step-by-step explanation:

nth term of an A.P = a+(n-1)d

5th term = a+(5-1)d = a+4d = 20-----(1)

Sum of n terms of an A.P =n/2{2a+(n-1)d

Sum of 5th and 7th term of A.P = 64

= a+(5-1)d + a+(7-1)d = 64

= a+4d+a+6d =64

= 2a + 10d = 64

Cancelling 2 from both the sides =

a+5d = 32---(2)

Subtracting eq(2) from eq(1)

a+5d = 32

-(a+4d = 20)

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d = 12