Question

25. Infan AP the third term is 21 and the ninth term is 39. Find the sum of the first twelve terms.​

Answer 1

Solution!!

The third term and the ninth term of an AP is 21 and 39, respectively.

a + 2d = 21...(1)

a + 8d = 39...(2)

Subtracting (1) and (2),

a - a + 2d - 8d = 21 - 39

-6d = -18

d = 3

Putting the value of d in (1)

a + 2d = 21

a + 2(3) = 21

a + 6 = 21

a = 15

Sₙ = n/2 (2a + (n - 1)d)

S₁₂ = 12/2 (2(15) + (12 - 1)3)

S₁₂ = 6(30 + (11)3)

S₁₂ = 6(30 + 33)

S₁₂ = 6(63)

S₁₂ = 378

Hence, the sum of first 12 terms is 378.

Answer 2

Step-by-step explanation:

a3=21,

a+2d=21.... (1)

a9=39,

a+8d=39....(2)

from equation 1 and 2 we get

a+2d=21

-a+8d=39

=-6d=-18

d=3

a=15

Sn = n/2{2a+(n-1)×d}

= 12/2{2×15+(12-1)×3}

= 6{30+11×3}

= 6{30+33}

= 6×63

Sn = 378