Question

If the sum of the first 3 terms of an AP is 20 and product of the First three terms is 150. Find the first term.

Answer 1

Answer:

Fragmentation, also known as splitting and a method of reproduction is seen in many organisms such as in bacteria: filamentous cyanobacteria, in fungi like molds, lichens, many animals such as sponges, acoel flatworms, some annelid worms and sea stars.

Answer 2

Answer:

The sum of the first 10 terms of the AP is - 150 and the sum of the first 20 terms is 0150–550 = -700.

S10 = (10/2)[2a+(10–1)d] = -150, or

-30 = 2a + 9d, or

2a = -30–9d …(1)

S20 = -700 = (20/2)[2a+(20–1)d], or

-70 = 2a + 19d, or

2a = -70–19d …(2)

Equate (1) and (2),

-30–9d = -70–19d, or

10d = -40, or

d = -4.

From (1), 2a = -30+36 = 6, or a = 3.

The first term of the AP = 3 and the common ratio = -4. Or the AP is 3, -1, -5, -9,…