Question

In an AP the first term is 2 and the sum of the first 5 term is one fourth the sum of the next five terms. Find 20th term

Answer 1

Answer:

Step-by-step explanation:

sum of the next five terms.

Sum of next 5 terms=t6+t7+.....t10=S10−S5

⇒S5=14(S10−S5)...........(i)

We know that Sn=n2[2a+(n−1)d]

⇒S5=52[2×2+(5−1)d]

∴S5=10+10d and

S10=102[2×2+(10−1)d]

S10=5(4+9d)

∴ By substituting the values of S5andS10 in (i) we get

10+10d=14(20+45d−10−10d)

⇒40+40d=10+35d

⇒d=−6

We know that tn=a+(n−1)d

∴t20=2+(20−1)(−6)=−112

Answer 2

Hello!!

✍️Let d be the common difference of the A.P.

✍️Therefore, the A.P. is 2, 2 + d, 2 + 2d, 2 + 3d,

✍️Sum of first five terms = 10 + 10d

✍️Sum of next five terms = 10 + 35d

✍️According to the given condition, =>10+10d = 1/4(10+35d)

=>40+40d = 10+35d

=>30 = −5d

=>d = −6

✍️a20 = a+(20−1)d = 2+(19)(−6) = 2−114 = −112

Hence, the 20th term of the A.P. is –112.

Thanks!!❤