Question

In an AP the difference between the 18th term and 8th term is 20 and the first term is 3 find the sum of first 10 terms

Answer 1

Step-by-step explanation:

us define the sequence with first term b and common difference x

. The fourth term is thus b+3x, and the eighth term is b+7x.

Subtracting, we find their difference is 4x. Given that their difference is 20, the common difference is 5

Looking back, we can now rewrite the fourth term as b+15 and the eighth term as b+35. We have that b+35 = (11/2)(b+15)

. Expanding, we have b+35 = 11/2b+165/2. Multiplying everything by 2 we have 2b+70=11b+165. Solving, we get b=-95/9. Thus, the first term is -95/9 and the common difference is 5.

Answer 2

Answer:

120

Step-by-step explanation:

Given = difference between 18th term and 8thterm is 20,

$\boxed{a18-a8 = 20}$

$\boxed{first \: term \: , a = 3}$

$\boxed{a + 17d - a - 7d = 20}$

$\boxed{10 \: d = 20}$

$\boxed{d = 2}$

We know that,

$\boxed{Sn = \frac{n}{2} (2a + (n - 1)d}$

Putting the values of d,n and a

$\boxed{Sn = \frac{10}{2} (2 \times 3 + (10- 1)2)}$

$\boxed{Sn = \frac{10}{2} (6 + 18)}$

$\boxed{Sn = \frac{10}{2} (24)}$

$\boxed{Sn = 10 \times 12}$

$\boxed{Sn = 120}$

Hence the sum of the first 10 terms is 120