First term of an AP is 7 and the sum of it's first four terms is half the sum of it's next four terms.Find the sum of it's first 30 terms
Answers
Answer:
Step-by-step explanation:
Required Formula:
Sum of n terms in A.P., Sn =
Where
a = first term of an A.P.
d = common difference
n = no. of terms in an A.P.
The first term of an A.P. i.e., a = 7
It is given that the sum of the first four terms is half of the sum of the next four terms in an A.P., so we can write the eq. as,
Sum of the first 4 terms = ½ * [{Sum of all the 8 terms} – {sum of first 4 terms}]
⇒ S₄ = ½ * [S₈ – S₄]
Based on the formula and substituting the value of a, we get
⇒
⇒ [4{14 + 3d}] = [4{14 + 7d}] – [2{14 + 3d}]
⇒ [4{14 + 3d}] + [2{14 + 3d}] = [4{14 + 7d}]
⇒ [6{14 + 3d}] = [4{14 + 7d}]
⇒ [3{14 + 3d}] = [2{14 + 7d}]
⇒ 42 + 9d = 28 + 14d
⇒ 5d = 14
⇒ d =
⇒ d = 2.8
Thus,
The sum of the 30 terms is given by,
= S₃₀
=
= [15 * { 14 + (29 * 2.8)}]
= [15 * {14 + 81.2}]
= 15 * 95.2
= 1428
Answer:
First term of an AP is 7 and the sum of it's first four terms is half the sum of it's next four terms.Find the sum of it's first 30 terms