Question

The second term of an arithmetic sequence is 24 and the fifth trrm is 3 find the first term and the common difference

Answer 1

Hi there!


∵ 2ᴺᴰ term, a₂ = 24
∴ a + d = 24. --(i)

∵ 5ᵀᴴ term, a₅ = 3.
∴ a + 4d = 3. ---(ii)

Subtracting Eqn. (i) from (ii) :-

(a + 4d) - (a + d) = 3 - 24

a + 4d - a - d = - 21

3d = - 21

d =
`\frac {- 21}{3}`

d = - 7

∴ Common difference, d = - 7

Substitute d = -7 in eqn. (i) :-

a + d = 24

a + (-7) = 24

a - 7 = 24

a = 24 + 7

a = 31

∴ First term, a = 31

~ Hope it helps!