Find `S_n`, if `S_n` = 1.3 + 2.4 + 3.5 + … upto n terms.

Find 2 xx 6 + 4 xx 9 + 6 xx 12 + …… upto n terms.

Find the sum 3 + 33 + 333 + ….. Upto n term.

Find 3.7 + 5.10 + 7.13 + 9.16 + … upto 'n' term.

Find 2 + 22 + 222 + 2222 ……. Upto n terms

Find 1 xx 5 + 3 xx 7 + 5 xx 9 + 7 xx 11 .... upto n terms.

Prove the following by the method of induction for all n in N : 1.3 + 3.5 + 5.7 +... to n terms =n/3 (4n^2 + 6n - 1) .

Find the sum 8 + 88 + 888 + ….. Upto n term.

If (1xx3 + 2xx5 + 3xx7 + ….. upto n terms) / ( 1^3 + 2^3 + 3^3 + …… upto n terms) = 5/9, find the value of n.

Find the sum of 1^1 n + 2^2 (n - 1) + 3^2 (n - 2) + 4^2 (n -3) ……upto 'n' terms.

For a sequence, if S_n = 3(2^n - 1) , find the nth term. Hence show that it a G.P. Also find the common ratio.