Question

how many terms of the. a.p. 1,4,7......are needed to the sum 715?

Answer 1

n=22.

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Answer 2

Answer:

The number of terms in an A.P. is 22.

Step-by-step explanation:

Given : A.P. 1,4,7,...are needed to the sum 715.

To find : How many terms?

Solution :

We have given an A.P 1,4,7,...

The first term is a=1

The common difference is d=4-1=3

$S_n=715$

The formula to find sum of an A.P. is

$S_n=\frac{n}{2}[2a+(n-1)d]$

Substitute the values in the formula,

$715=\frac{n}{2}[2(1)+(n-1)3]$

$1430=n[2+3n-3]$

$1430=n[3n-1]$

$1430=3n^2-n$

$3n^2-n-1430=0$

Solving graphically the values of n are -21 and 22.

Refer the attached figure below.

Reject n=-21 and accept n=22.

The number of terms in an A.P. is 22.