Question

An Ap is such that 5 th term is three times the 2nd term.given further that the sum of the 5th,6th,7th,8th term is240,calculate the value of the first term.​

Answer 1

5

Explanation:

The general term of an arithmetic progression is ...

an = a1 +d(n -1)

where a1 is the first term and d is the common difference.

Here we are given that ...

a5 = 3×a2

a5 +a6 +a7 +a8 = 240

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In terms of a1 and d, these tell us ...

a1 +d(5 -1) = 3(a1 +d(2 -1))

a1 +4d = 3a1 +3d . . . . . eliminate parentheses

d = 2a1 . . . . . . . . . . . subtract a1+3d

and ...

(a1 +4d) +(a1 +5d) +(a1 +6d) +(a1 +7d) = 240

4a1 +22d = 240

Substituting for d, we have ...

4a1 +22(2a1) = 240

48a1 = 240

a1 = 240/48 = 5

The first term is 5.