Question

5th term and 6th term of an A.P are 6 and 5. Find the 100th term. Write 5th term in terms of a and d

Answer 1

Answer:

Let series

A1,A2,A3........An be in AP

Then we can say,

A2 = A1+ d {where d is common difference; d = (a2-a1)}

Similarly,

nth term = First term + d *(n-1)

{where n is total number of terms}

Here,

A5 = 5 and A6 = 6

Therefore, d=(6-5)=1

Since we know,

A5 = A1 + d*(n-1)

=> 5 = A1 + 1*(5-1)

=> 5= A1 + 4

=> A1=1 -------(1)

Similarly,

A11 = A1 + d*(11-1)

=> A11 = 1 + 1*(10) { from eq(1)}

A11 = 11

Alternative:-

Since, the Common Diff is 1

and 5th & 6th term are 5 and 6 respectively.

Hence the 11th term will be 11.

Thank You

Answer 2

Answer:

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