Question

The first & the last term of an A.P are 17 & 350 respectively. If the C.d is 9 how many terms are there & what is their sum?

A. n ₌ 30, Sum ₌ 5505
B. n ₌ 42, Sum ₌ 7707
C. n ₌ 38, Sum ₌ 6973
D. n ₌ 34, Sum ₌ 6239

Answer 1

To find the number of terms (n) and the sum of the terms in an arithmetic progression (AP), use the formulas n = (last term - first term) / common difference + 1 and S = n / 2 * (first term + last term).

Step-by-step explanation:

To find the number of terms (n) and the sum of the terms in an arithmetic progression (AP), we can use the formula:

n = (last term - first term) / common difference + 1

In this case, the first term (a) is 17, the last term (l) is 350, and the common difference (d) is 9. Plugging these values into the formula, we get:

n = (350 - 17) / 9 + 1 = 34

The number of terms in the AP is 34. Now, to find the sum of the terms (S), we can use the formula:

S = n / 2 * (first term + last term)

Plugging in the values we know, we get:

S = 34 / 2 * (17 + 350) = 6239

So, the answer is D. There are 34 terms in the AP and the sum of the terms is 6239.