Question

Find the sum of the first 15 terms of each of the following sequences having nth term as

(i) a_n = 3 + 4n

(ii) b_n = 5 + 2n

(iii) x_n = 6 − n

(iv) y_n = 9 − 5n

Answer 1

(i) Here, we are given an A.P. whose n^th term is given by the following expression, . We need to find the sum of first 15 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula,

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using in the given equation for n^th term of A.P.

Now, the last term (l) or the n^th term is given

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

Therefore, the sum of the 15 terms of the given A.P. is.

(ii) Here, we are given an A.P. whose n^th term is given by the following expression

We need to find the sum of first 15 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula,

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using in the given equation for n^th term of A.P.

Now, the last term (l) or the n^th term is given

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

Therefore, the sum of the 15 terms of the given A.P. is.

(iii) Here, we are given an A.P. whose n^th term is given by the following expression, . We need to find the sum of first 15 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula,

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using in the given equation for n^th term of A.P.

Now, the last term (l) or the n^th term is given

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

Therefore, the sum of the 15 terms of the given A.P. is.

(iv) Here, we are given an A.P. whose n^th term is given by the following expression, . We need to find the sum of first 15 terms.

So, here we can find the sum of the n terms of the given A.P., using the formula,

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using in the given equation for n^th term of A.P.

Now, the last term (l) or the n^th term is given

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,

Therefore, the sum of the 15 terms of the given A.P. is.