The 2nd, 31st and last term of an AP are 7\(\frac { 2 }{ 4 } \) , \(\frac { 1 }{ 2 } \) and - 6 \(\frac { 1 }{ 2 } \), respectively. Find the first term and the number of terms.

4

(a)

Find the number of terms common to the two AP's 3, 7, 11, .... 407 and 2, 9, 16, ....709.

4

(a)

Find  the middle terms in the AP 20, 16, 12, ....., -176.

4

(a)

Find the 15th term from the end of the AP 3, 5, 7, 9, ......, 201.

4

(a)

Three numbers are in AP. If their sum is 27 and the product 648, find the numbers.

4

(a)

The sums of n terms of two arithmetic progressions are on the ratio 5n + 4; 9n + 6. Find the ratio of their 18^th terms.

5

(a)

Sum of the first p, q and r terms of an A.P. are a, b and c respectively. Prove that \(\frac { a }{ p } (q-r)+\frac { b }{ q } (r-p)+\frac { c }{ r } (p-q)=0\)

5

(a)

The ratio of the sum of m and n terms of an A.p. is m²:n². Show that the ratio of m^th and n^th term is (2m - 1): (2n - 1).

5

(a)

The difference between any two consecutive interior angles of a polgon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

5

(a)

Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

5

(a)

Find the Value of n so that \(\frac { { a }^{ n+1 }+b^{ n+1 } }{ { a }^{ n }+{ b }^{ n } } \) may be the geometric mean between a and b 

5

(a)