How many terms of A P 18,15,12, are needed to give the sum 45 Explain - Maths - Arithmetic Progressions

Question

How many terms of A P 18,15,12, are needed to give the sum 45?
Explain the double answer
What is the explaination for the double answer?

Vimala · Accepted Answer

Consider the terms of the A P 18, 15, 12, 9, Here the first term, a = 18, d = -3; We need to find the number of terms of the above A P so that the sum will give 45 The formula for sum of A P is $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ Thus, the sum of A P is $45 = \frac{n}{2} [2 \times 18 + (n - 1) (- 3)] 90 = 36 n - 3 n (n - 1) 30 = 12 n - n (n - 1) n^{2} - 13 n + 30 = 0 n^{2} - 10 n - 3 n + 30 = 0 n (n - 10) - 3 (n - 10) = 0 (n - 3) (n - 10) = 0 n - 3 = 0 o r n - 10 = 0 n = 3 o r n = 10$ Thus, the sum of first 3 terms or the sum of first 10 terms will be 45 But, Check your question for the term 'double answer'

How many terms of A.P. 18,15,12,... are needed to give the sum 45? Explain the double answer. What is the explaination for the double answer?

How many terms of A.P. 18,15,12,... are needed to give the sum 45? Explain the double answer.

What is the explaination for the double answer?