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

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 =

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!

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12