Question

Find the common difference of an AP whose first term is 5
and the sum of the first four terms is half the sum of the next
four terms.​

Answer 1

Answer:

Answer:

Given :-

First Term = 5

Sum of first 4 terms = half of next two terms

To Find :-

Common Difference

Solution :-

We know that

\large \sf \: Sum \: = \dfrac{n}{2} \bigg(a + l \bigg) \:Sum=

2

n

(a+l)

Now,

Sum = 4/2 (5 + 5 + 3d)

Sum = 2(5 + 5 + 3d)

Sum = 2(10 + 3d)

Now,

Sum = 4/2{(5 + 4d) + (5 + 7d)}

Sum = 2{(5 + 4d) + (5 + 7d)}

Sum = 2{5 + 5 + 4d + 7d}

Sum = 2{10 + 11d}

Now

2(10 + 3d) = 2(10 + 11d)/2

Since it's half

20 + 6d = 10 + 11d

20 - 10 = 11d - 6d

10 = 5d

10/5 = d

\dag{ \textsf{ \textbf{ \pink{ \underline{Difference = 2}}}}}†

Difference = 2

Answer 2

Answer:

Let d is common difference of AP

Now first 4 terms are 5, 5+d, 5+2d, 5+3d

and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

5 + 5+d + 5+2d + 5+3d= (5+4d + 5+5d + 5+6d + 5+7d)/2

20+6d= (20+22d)/2

20+6d=10+11d

d=2

Hence, the common difference of the given A.P. is 2