Question

Sum of first 40 terms of ap=200 and the sum of next 40 terms =3500.find the first term

Answer 1

Answer:

Step-by-step explanation:

S=3+4+8+9+13+14+18+19+....40 terms

=7+17+27+37+...20 terms

it is in A.P

∴s=

2

20

​

[2×7+(20−1)10]

=10(14+190)

=10×204

=20×102

as s=(102)m

⇒20×102=102×m

m=20

Answer 2

Answer:

-35 7/32

Step-by-step explanation:

Given AP with sum of first 40 terms= 200 and sum of next 40 terms= 3500

First term=?

========

Sum of second 40 terms= sum of first 80 terms - sum of first 40 terms

S₄₀

• 1/2×40×(2a+39d) = 200

• 20×(2a+39d)=200
• 2a+39d=10   -----  (1)

S₈₀ - S₄₀

• 1/2×80×(2a+79d) - 1/2×40×(2a+39d) = 3500

• 40×(2a+79d)- 20×(2a+39d)=3500
• 8a+316d-4a-78d=350
• 4a+238d=350  -----  (2)

(2) - (1) × 2

• 4a+238d -4a- 78d=350 - 20
• 160d=330
• d=330/160
• d=33/16

The common difference is known, let's find the first term:

• 2a+39d=10
• 2a+ 39×33/16=10
• 2a= 10 - 1287/16
• 2a= - 1127/16
• a= - 1127/32 = - 35 7/32

• a= -35 7/32

The first term is : -35 7/32